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Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

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Abstract

The review summarises recent theoretical achievements and observational manifestations of a new, recently discovered type of nonlinear oscillations in multi-component plasmas, namely super-nonlinear periodic waves and super-nonlinear solitary waves (supersolitons). Both are characterised by a non-trivial topology of their phase portraits, highly anharmonic profile shapes, extremely long periods, and large amplitudes. Based upon multi-fluid magnetohydrodynamic plasma models, examples of ion-acoustic and Alfvén super-nonlinear waves are considered. A multi-component nature of the plasma was revealed to be a crucial condition for the existence of these super-nonlinear waves, with the complexity of the system growing with the number of plasma species accounted for in the model. A minimum number of plasma components which allow for the existence of super-nonlinear waves are also discussed. From the observational point of view, typical signatures of periodic super-nonlinear waves are manifested, for example, in the oscillatory processes operating in the magnetised plasma of the solar corona and ground-based plasma machines. Super-nonlinear solitary structures (supersolitons) of an electrostatic origin are recognised in the Earth’s magnetosphere, laboratory experiments with chemically active plasmas, and numerical simulations.

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References

  • L. Abbo, L. Ofman, S.K. Antiochos, V.H. Hansteen, L. Harra, Y.-K. Ko, G. Lapenta, B. Li, P. Riley, L. Strachan, R. von Steiger, Y.-M. Wang, Slow solar wind: observations and modeling. Space Sci. Rev. 201, 55–108 (2016)

    ADS  Google Scholar 

  • M. Akbari-Moghanjoughi, Double-wells and double-layers in dusty Fermi-Dirac plasmas: Comparison with the semiclassical Thomas-Fermi counterpart. Phys. Plasmas 17(12), 123709 (2010)

    ADS  Google Scholar 

  • M. Akbari-Moghanjoughi, Universal aspects of localized excitations in graphene. J. Appl. Phys. 114(7), 073302 (2013)

    ADS  Google Scholar 

  • M. Akbari-Moghanjoughi, Large-amplitude solitons in gravitationally balanced quantum plasmas. Phys. Plasmas 21(8), 082707 (2014)

    ADS  Google Scholar 

  • M. Ansar Mahmood, S. Mahmood, M. M. Arshad, H. Saleem, Low frequency solitary waves in magnetized electron positron ion plasmas. Chin. Phys. Lett. 22, 632–635 (2005)

    ADS  Google Scholar 

  • W.I. Axford, J.F. McKenzie, The origin of high speed solar wind streams, in Solar Wind Seven Colloquium, ed. by E. Marsch, R. Schwenn (Pergamon Press, Oxford, 1992), pp. 1–5

    Google Scholar 

  • T.K. Baluku, M.A. Hellberg, I. Kourakis, N.S. Saini, Dust ion acoustic solitons in a plasma with kappa-distributed electrons. Phys. Plasmas 17(5), 053702 (2010)

    ADS  Google Scholar 

  • A.R. Barakat, R.W. Schunk, Transport equations for multicomponent anisotropic space plasmas–a review. Plasma Phys. 24, 389–418 (1982)

    ADS  MathSciNet  Google Scholar 

  • R. Bostrom, G. Gustafsson, B. Holback, G. Holmgren, H. Koskinen, Characteristics of solitary waves and weak double layers in the magnetospheric plasma. Phys. Rev. Lett. 61, 82–85 (1988)

    ADS  Google Scholar 

  • T.J. Bridges, Spatial Hamiltonian Structure, Energy Flux and the Water-Wave Problem. Proc. R. Soc. Lond. Ser. A 439, 297–315 (1992)

    ADS  MathSciNet  MATH  Google Scholar 

  • T.J. Bridges, P.E. Hydon, S. Reich, Vorticity and symplecticity in Lagrangian fluid dynamics. J. Phys. A Math. Gen. 38, 1403–1418 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  • R.A. Cairns, A.A. Mamum, R. Bingham, R. Boström, R.O. Dendy, C.M.C. Nairn, P.K. Shukla, Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712 (1995)

    ADS  Google Scholar 

  • Y. Chen, Z.-Y. Li, W. Liu, Z.-D. Shi, Solitary kinetic Alfvén waves in the inertial limit region. Phys. Plasmas 7, 371–374 (2000)

    ADS  Google Scholar 

  • R. Chin, E. Verwichte, G. Rowlands, V.M. Nakariakov, Self-organization of magnetoacoustic waves in a thermally unstable environment. Phys. Plasmas 17(3), 032107 (2010)

    ADS  Google Scholar 

  • C.R. Choi, D.-Y. Lee, Solitary Alfvén waves in a dusty plasma. Phys. Plasmas 14(5), 052304 (2007)

    ADS  Google Scholar 

  • C.R. Choi, C.-M. Ryu, D.-Y. Lee, N.C. Lee, Y.-H. Kim, Dust ion acoustic solitary waves in a magnetized dusty plasma with anisotropic ion pressure. Phys. Lett. A 364, 297–303 (2007)

    ADS  Google Scholar 

  • I.L. Cooney, M.T. Gavin, I. Tao, K.E. Lonngren, A two-dimensional soliton in a positive ion-negative ion plasma. IEEE Trans. Plasma Sci. 19, 1259–1266 (1991a)

    ADS  Google Scholar 

  • J.L. Cooney, M.T. Gavin, K.E. Lonngren, Radiation of ion acoustic waves in a dispersive positive ion-negative ion plasma. IEEE Trans. Plasma Sci. 19, 545–547 (1991b)

    ADS  Google Scholar 

  • R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)

    MathSciNet  MATH  Google Scholar 

  • R.C. Davidson, Methods in Nonlinear Plasma Theory (Academic Press, New York, 1972)

    Google Scholar 

  • H.G. Demars, R.W. Schunk, A multi-ion generalized transport model of the polar wind. J. Geophys. Res. 99, 2215–2226 (1994)

    ADS  Google Scholar 

  • A.E. Dubinov, Gas-dynamic approach in the nonlinear theory of ion acoustic waves in a plasma: an exact solution. J. Appl. Mech. Tech. Phys. 48, 621–628 (2007a)

    ADS  Google Scholar 

  • A.E. Dubinov, Theory of nonlinear space charge waves in neutralized electron flows: gas-dynamic approach. Plasma Phys. Rep. 33, 210–217 (2007b)

    ADS  Google Scholar 

  • A.E. Dubinov, On a widespread inaccuracy in defining the mach number of solitons in a plasma. Plasma Phys. Rep. 35, 991–993 (2009)

    ADS  Google Scholar 

  • A.E. Dubinov, I.D. Dubinova, How can one solve exactly some problems in plasma theory. J. Plasma Phys. 71, 715–728 (2005)

    ADS  Google Scholar 

  • A.E. Dubinov, D.Y. Kolotkov, Interpretation of ion-acoustic solitons of unusual form in experiments in SF6–Ar plasma. High Energy Chem. 46, 349–353 (2012a)

    Google Scholar 

  • A.E. Dubinov, D.Y. Kolotkov, Ion-acoustic super solitary waves in dusty multispecies plasmas. IEEE Trans. Plasma Sci. 40, 1429–1433 (2012b)

    ADS  Google Scholar 

  • A.E. Dubinov, D.Y. Kolotkov, Ion-acoustic supersolitons in plasma. Plasma Phys. Rep. 38, 909–912 (2012c)

    ADS  Google Scholar 

  • A.E. Dubinov, M.A. Sazonkin, Nonlinear adiabatic models of ion-acoustic waves in dust plasma. J. Tech. Phys. 53, 1129–1140 (2008)

    ADS  Google Scholar 

  • A.E. Dubinov, M.A. Sazonkin, Supernonlinear ion-acoustic waves in a dusty plasma. Phys. Wave Phenom. 21, 118–128 (2013)

    ADS  Google Scholar 

  • A.E. Dubinov, A.A. Dubinova, M.A. Sazonkin, Nonlinear theory of the isothermal ion-acoustic waves in the warm degenerate plasma. J. Commun. Technol. Electron. 55, 907–920 (2010)

    Google Scholar 

  • A.E. Dubinov, D.Y. Kolotkov, M.A. Sazonkin, Nonlinear ion acoustic waves in a quantum degenerate warm plasma with dust grains. Plasma Phys. Rep. 37, 64–74 (2011)

    ADS  Google Scholar 

  • A.E. Dubinov, D.Y. Kolotkov, M.A. Sazonkin, Supernonlinear waves in plasma. Plasma Phys. Rep. 38, 833–844 (2012)

    ADS  Google Scholar 

  • I.D. Dubinova, Application of the Lambert W function in mathematical problems of plasma physics. Plasma Phys. Rep. 30, 872–877 (2004)

    ADS  Google Scholar 

  • D. Dutta, B. Sahu, Nonlinear structures in an ion-beam plasmas including dust impurities with nonthermal nonextensive electrons. Commun. Theor. Phys. 68, 117 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  • D. Dutta, P. Singha, B. Sahu, Interlaced linear-nonlinear wave propagation in a warm multicomponent plasma. Phys. Plasmas 21(12), 122308 (2014)

    ADS  Google Scholar 

  • M.M. Echim, J. Lemaire, Ø. Lie-Svendsen, A review on solar wind modeling: kinetic and fluid aspects. Surv. Geophys. 32, 1–70 (2011)

    ADS  Google Scholar 

  • S.A. El-Wakil, E.M. Abulwafa, A.A. Elhanbaly, Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions. Phys. Plasmas 24(7), 073705 (2017)

    ADS  Google Scholar 

  • R.E. Ergun, C.W. Carlson, J.P. McFadden, F.S. Mozer, L. Muschietti, I. Roth, R.J. Strangeway, Debye-scale plasma structures associated with magnetic-field-aligned electric fields. Phys. Rev. Lett. 81, 826–829 (1998)

    ADS  Google Scholar 

  • G.D. Fleishman, A.T. Altyntsev, N.S. Meshalkina, Microwave signature of relativistic positrons in solar flares. Publ. Astron. Soc. Jpn. 65, S7 (2013)

    ADS  Google Scholar 

  • J.R. Franz, P.M. Kintner, J.S. Pickett, L.-J. Chen, Properties of small-amplitude electron phase-space holes observed by Polar. J. Geophys. Res. (Space Phys) 110, A9212 (2005)

    ADS  Google Scholar 

  • S.B. Ganguli, The polar wind. Rev. Geophys. 34, 311–348 (1996)

    ADS  Google Scholar 

  • S.S. Ghosh, G.S. Lakhina, Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas. Nonlinear Process. Geophys. 11, 219–228 (2004)

    ADS  Google Scholar 

  • S.S. Ghosh, A.N. Sekar Iyengar, Effect of cooler electrons on a compressive ion acoustic solitary wave in a warm ion plasma—forbidden regions, double layers, and supersolitons. Phys. Plasmas 21(8), 082104 (2014)

    ADS  Google Scholar 

  • M.V. Goldman, M.M. Oppenheim, D.L. Newman, Theory of localized bipolar wave-structures and nonthermal particle distributions in the auroral ionosphere. Nonlinear Process. Geophys. 6, 221–228 (1999)

    ADS  Google Scholar 

  • G. Gustafsson, M. André, T. Carozzi, A.I. Eriksson, C.-G. Fälthammar, R. Grard, G. Holmgren, J.A. Holtet, N. Ivchenko, T. Karlsson, Y. Khotyaintsev, S. Klimov, H. Laakso, P.-A. Lindqvist, B. Lybekk, G. Marklund, F. Mozer, K. Mursula, A. Pedersen, B. Popielawska, S. Savin, K. Stasiewicz, P. Tanskanen, A. Vaivads, J.-E. Wahlund, First results of electric field and density observations by Cluster EFW based on initial months of operation. Ann. Geophys. 19, 1219–1240 (2001)

    ADS  Google Scholar 

  • T. Hada, C.F. Kennel, B. Buti, Stationary nonlinear Alfven waves and solitons. J. Geophys. Res. 94, 65–77 (1989)

    ADS  Google Scholar 

  • M.A. Hellberg, T.K. Baluku, F. Verheest, I. Kourakis, Dust-acoustic supersolitons in a three-species dusty plasma with kappa distributions. J. Plasma Phys. 79, 1039–1043 (2013)

    ADS  Google Scholar 

  • N.E. Huang, Z. Wu, A review on Hilbert–Huang transform: method and its applications to geophysical studies. Rev. Geophys. 46, RG2006 (2008)

    ADS  Google Scholar 

  • N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.-C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A 454, 903–998 (1998)

    ADS  MathSciNet  MATH  Google Scholar 

  • P.E. Hydon, Multisymplectic conservation laws for differential and differential-difference equations. Proc. R. Soc. Lond. Ser. A 461, 1627–1637 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  • H. Ikezi, Experiments on ion-acoustic solitary waves. Phys. Fluids 16, 1668–1675 (1973)

    ADS  Google Scholar 

  • E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos, 2nd edn. (Cambridge University Press, Cambridge, 2000)

    MATH  Google Scholar 

  • P.A. Isenberg, J.V. Hollweg, On the preferential acceleration and heating of solar wind heavy ions. J. Geophys. Res. 88, 3923–3935 (1983)

    ADS  Google Scholar 

  • I.D. Kaganovich, L.D. Tsendin, Formation of discontinuities in multistage evolution associated with diffusion of a multicomponent weakly ionized hot-electron plasma. Plasma Phys. Rep. 19, 645–650 (1993)

    ADS  Google Scholar 

  • I.D. Kaganovich, D.J. Economou, B.N. Ramamurthi, V. Midha, Negative ion density fronts during ignition and extinction of plasmas in electronegative gases. Phys. Rev. Lett. 84, 1918–1921 (2000)

    ADS  Google Scholar 

  • B. Kakad, A. Kakad, Y. Omura, Nonlinear evolution of ion acoustic solitary waves in space plasmas: fluid and particle-in-cell simulations. J. Geophys. Res. (Space Phys.) 119, 5589–5599 (2014)

    ADS  Google Scholar 

  • A. Kakad, A. Lotekar, B. Kakad, First-ever model simulation of the new subclass of solitons “supersolitons” in plasma. Phys. Plasmas 23(11), 110702 (2016)

    ADS  Google Scholar 

  • H. Kaur, T. Singh, Gill. Study of large amplitude solitons in multispecies plasma with non-Maxwellian electrons. J. Phys. Conf. Ser. 208(1), 012080 (2010)

    Google Scholar 

  • D.Y. Kolotkov, V.M. Nakariakov, G. Rowlands, Nonlinear oscillations of coalescing magnetic flux ropes. Phys. Rev. E 93(5), 053205 (2016)

    ADS  Google Scholar 

  • I.V. Konikov, O.A. Gorbachev, G.V. Khazanov, A.A. Chernov, Hydrodynamical equations for thermal electrons taking into account their scattering on ion-cyclotron waves in the outer plasmasphere of the earth. Planet. Space Sci. 37, 1157–1168 (1989)

    ADS  Google Scholar 

  • H.H. Kuehl, K. Imen, Ion-acoustic solitary waves near double layers. IEEE Trans. Plasma Sci. 13, 37–40 (1985)

    ADS  Google Scholar 

  • G.S. Lakhina, S.V. Singh, A.P. Kakad, Ion acoustic solitons/double layers in two-ion plasma revisited. Phys. Plasmas 21(6), 062311 (2014)

    ADS  Google Scholar 

  • I. Lopes, D. Passos, M. Nagy, K. Petrovay, Oscillator models of the solar cycle. Towards the development of inversion methods. Space Sci. Rev. 186, 535–559 (2014)

    ADS  Google Scholar 

  • A. Lotekar, A. Kakad, B. Kakad, Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons. Phys. Plasmas 23(10), 102108 (2016)

    ADS  Google Scholar 

  • Q.M. Lu, D.Y. Wang, S. Wang, Generation mechanism of electrostatic solitary structures in the Earth’s auroral region. J. Geophys. Res. (Space Phys.) 110, A3223 (2005)

    ADS  Google Scholar 

  • G.O. Ludwig, J.L. Ferreira, Y. Nakamura, Observation of ion-acoustic rarefaction solitons in a multicomponent plasma with negative ions. Phys. Rev. Lett. 52, 275–278 (1984)

    ADS  Google Scholar 

  • R.L. Mace, J.F. McKenzie, G.M. Webb, Conservation laws for steady flow and solitons in a multifluid plasma revisited. Phys. Plasmas 14(1), 012310 (2007)

    ADS  Google Scholar 

  • S.K. Maharaj, R. Bharuthram, S.V. Singh, G.S. Lakhina, Existence domains of dust-acoustic solitons and supersolitons. Phys. Plasmas 20(8), 083705 (2013)

    ADS  Google Scholar 

  • A.A. Mamun, P.K. Shukla, Arbitrary amplitude solitary waves and double layers in an ultra-relativistic degenerate dense dusty plasma. Phys. Lett. A 374, 4238–4241 (2010)

    ADS  MATH  Google Scholar 

  • W. Masood, H.A. Shah, N.L. Tsintsadze, M.N.S. Qureshi, Dust Alfven ordinary and cusp solitons and modulational instability in a self-gravitating magneto-radiative plasma. Eur. Phys. J. D 59, 413–419 (2010)

    ADS  Google Scholar 

  • J.F. McKenzie, E. Dubinin, K. Sauer, T.B. Doyle, The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint. J. Plasma Phys. 70, 431–462 (2004)

    ADS  Google Scholar 

  • J.F. McKenzie, R.L. Mace, T.B. Doyle, Nonlinear Hall MHD and electrostatic ion-cyclotron stationary waves: a Hamiltonian-geometric viewpoint. J. Plasma Phys. 73, 687–700 (2007)

    ADS  Google Scholar 

  • C.A. Mendoza-Briceño, S.M. Russel, A.A. Mamun, Large amplitude electrostatic solitary structures in a hot non-thermal dusty plasma. Planet. Space Sci. 48, 599–608 (2000)

    ADS  Google Scholar 

  • Y.C. Mo, R.A. Kishek, D. Feldman, I. Haber, B. Beaudoin, P.G. O’Shea, J.C.T. Thangaraj, Experimental observations of soliton wave trains in electron beams. Phys. Rev. Lett. 110(8), 084802 (2013)

    ADS  Google Scholar 

  • F.S. Mozer, R. Ergun, M. Temerin, C. Cattell, J. Dombeck, J. Wygant, New features of time domain electric-field structures in the auroral acceleration region. Phys. Rev. Lett. 79, 1281–1284 (1997)

    ADS  Google Scholar 

  • K. Murawski, Stability of modified Korteweg-de Vries waves. Aust. J. Phys. 40, 593–599 (1987)

    ADS  MATH  Google Scholar 

  • R.J. Murphy, B. Kozlovsky, G.H. Share, Radioactive positron emitter production by energetic alpha particles in solar flares. Astrophys. J. Suppl. 215, 18 (2014)

    ADS  Google Scholar 

  • Y. Nakamura, Experiments on ion-acoustic solitons in plasmas. IEEE Trans. Plasma Sci. 10, 180–195 (1982)

    ADS  Google Scholar 

  • Y. Nakamura, I. Tsukabayashi, Modified Korteweg-de Vries in-acoustic solitons in a plasma. J. Plasma Phys. 34, 401–415 (1985)

    ADS  Google Scholar 

  • Y. Nakamura, J.L. Ferreira, G.O. Ludwig, Experiments on ion-acoustic rarefactive solitons in a multi-component plasma with negative ions. J. Plasma Phys. 33, 237–248 (1985)

    ADS  Google Scholar 

  • V.M. Nakariakov, V.F. Melnikov, Quasi-periodic pulsations in solar flares. Space Sci. Rev. 149, 119–151 (2009)

    ADS  Google Scholar 

  • V.M. Nakariakov, E. Verwichte, Coronal waves and oscillations. Living Rev. Sol. Phys. 2, 3–65 (2005)

    ADS  Google Scholar 

  • V.M. Nakariakov, A.R. Inglis, I.V. Zimovets, C. Foullon, E. Verwichte, R. Sych, I.N. Myagkova, Oscillatory processes in solar flares. Plasma Phys. Control. Fusion 52(12), 124009 (2010)

    ADS  Google Scholar 

  • V.M. Nakariakov, V. Pilipenko, B. Heilig, P. Jelínek, M. Karlický, D.Y. Klimushkin, D.Y. Kolotkov, D.-H. Lee, G. Nisticò, T. Van Doorsselaere, G. Verth, I.V. Zimovets, Magnetohydrodynamic oscillations in the solar corona and Earth’s magnetosphere: towards consolidated understanding. Space Sci. Rev. 200, 75–203 (2016)

    ADS  Google Scholar 

  • C.P. Olivier, S.K. Maharaj, R. Bharuthram, Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion- and two electron species. Phys. Plasmas 22(8), 082312 (2015)

    ADS  Google Scholar 

  • C.P. Olivier, F. Verheest, S.K. Maharaj, Small-amplitude supersolitons near supercritical plasma compositions. J. Plasma Phys. 83(4), 905830403 (2017)

    Google Scholar 

  • D.J. Pascoe, C.R. Goddard, G. Nisticò, S. Anfinogentov, V.M. Nakariakov, Damping profile of standing kink oscillations observed by SDO/AIA. Astron. Astrophys. 585, L6 (2016)

    ADS  Google Scholar 

  • A. Paul, A. Bandyopadhyay, Dust ion acoustic solitary structures in presence of nonthermal electrons and isothermal positrons. Astrophys. Space Sci. 361, 172 (2016)

    ADS  Google Scholar 

  • I. Paul, S. Chandra, S. Chattopadhyay, S.N. Paul, W-type ion-acoustic solitary waves in plasma consisting of cold ions and nonthermal electrons. Indian J. Phys. 90, 1195–1205 (2016)

    ADS  Google Scholar 

  • S.I. Popel, A.A. Gisko, Charged dust and shock phenomena in the solar system. Nonlinear Process. Geophys. 13, 223–229 (2006)

    ADS  Google Scholar 

  • O.R. Rufai, Auroral electrostatic solitons and supersolitons in a magnetized nonthermal plasma. Phys. Plasmas 22(5), 052309 (2015)

    ADS  Google Scholar 

  • O.R. Rufai, R. Bharuthram, S.V. Singh, G.S. Lakhina, Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons. Phys. Plasmas 21(8), 082304 (2014)

    ADS  Google Scholar 

  • O.R. Rufai, R. Bharuthram, S.V. Singh, G.S. Lakhina, Effect of excess superthermal hot electrons on finite amplitude ion-acoustic solitons and supersolitons in a magnetized auroral plasma. Phys. Plasmas 22(10), 102305 (2015)

    ADS  Google Scholar 

  • O.R. Rufai, R. Bharuthram, S.V. Singh, G.S. Lakhina, Nonlinear low frequency electrostatic structures in a magnetized two-component auroral plasma. Phys. Plasmas 23(3), 032309 (2016a)

    ADS  Google Scholar 

  • O.R. Rufai, R. Bharuthram, S.V. Singh, G.S. Lakhina, Obliquely propagating ion-acoustic solitons and supersolitons in four-component auroral plasmas. Adv. Space Res. 57, 813–820 (2016b)

    ADS  Google Scholar 

  • N.M. Ryskin, D.I. Trubetskov, Nonlinear Waves (Fizmatlit, Moscow, 2000) (in Russian)

    Google Scholar 

  • R.W. Schunk, Mathematical structure of transport equations for multispecies flows. Rev. Geophys. Space Phys. 15, 429–445 (1977)

    ADS  Google Scholar 

  • G.H. Share, R.J. Murphy, D.M. Smith, R.A. Schwartz, R.P. Lin, RHESSI e+-e− annihilation radiation observations: implications for conditions in the flaring solar chromosphere. Astrophys. J. Lett. 615, L169–L172 (2004)

    ADS  Google Scholar 

  • S.V. Singh, G.S. Lakhina, Ion-acoustic supersolitons in the presence of non-thermal electrons. Commun. Nonlinear Sci. Numer. Simul. 23, 274–281 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  • B.M. Smirnov, Physics of ball lightning. Phys. Rep. 224, 151–236 (1993)

    ADS  Google Scholar 

  • S.V. Steffy, S.S. Ghosh, Existence domain of the compressive ion acoustic super solitary wave in a two electron temperature warm multi-ion plasma. Phys. Plasmas 24(10), 102111 (2017)

    ADS  Google Scholar 

  • W. Swider, Electron loss and the determination of electron concentrations in the D-region. Pure Appl. Geophys. 127, 403–414 (1988)

    ADS  Google Scholar 

  • W. Swider, Sodium chemistry—a brief review and two new mechanisms for sudden sodium layers. Planet. Space Sci. 40, 247–253 (1992)

    ADS  Google Scholar 

  • T. Takeuchi, S. Iizuka, N. Sato, Ion acoustic shocks formed in a collisionless plasma with negative ions. Phys. Rev. Lett. 80, 77–80 (1998)

    ADS  Google Scholar 

  • R.J. Taylor, K.R. MacKenzie, H. Ikezi, A large double plasma device for plasma beam and wave studies. Rev. Sci. Instrum. 43, 1675–1678 (1972)

    ADS  Google Scholar 

  • M. Temerin, K. Cerny, W. Lotko, F.S. Mozer, Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 1175–1179 (1982)

    ADS  Google Scholar 

  • C.-Y. Tu, A solar wind model with the power spectrum of Alfvenic fluctuations. Solar Phys. 109, 149–186 (1987)

    ADS  Google Scholar 

  • C.-Y. Tu, E. Marsch, Two-fluid model for heating of the solar corona and acceleration of the solar wind by high-frequency Alfven waves. Solar Phys. 171, 363–391 (1997)

    ADS  Google Scholar 

  • S.R. Valluri, D.J. Jeffrey, R.M. Corless, Tutorial/Article didactique: some applications of the Lambert W function to physics. Can. J. Phys. 78, 823 (2000)

    ADS  Google Scholar 

  • T. Van Doorsselaere, E.G. Kupriyanova, D. Yuan, Quasi-periodic pulsations in solar and stellar flares: an overview of recent results. Sol. Phys. 291, 3143–3164 (2016)

    ADS  Google Scholar 

  • I.Y. Vasko, O.V. Agapitov, F. Mozer, A.V. Artemyev, D. Jovanovic, Magnetic field depression within electron holes. Geophys. Res. Lett. 42, 2123–2129 (2015)

    ADS  Google Scholar 

  • F. Verheest, Nonlinear acoustic waves in nonthermal plasmas with negative and positive dust. Phys. Plasmas 16(1), 013704 (2009)

    ADS  MathSciNet  Google Scholar 

  • F. Verheest, Dust-acoustic solitary modes in plasmas with isothermal and nonthermal ions: Polarity switches and coexistence domains. Phys. Plasmas 18(8), 083701 (2011)

    ADS  MathSciNet  Google Scholar 

  • F. Verheest, Electrostatic nonlinear supersolitons in dusty plasmas. J. Plasma Phys. 80, 787–793 (2014)

    ADS  Google Scholar 

  • F. Verheest, M.A. Hellberg, Electrostatic supersolitons and double layers at the acoustic speed. Phys. Plasmas 22(1), 012301 (2015)

    ADS  Google Scholar 

  • F. Verheest, M.A. Hellberg, G.J. Gray, R.L. Mace, Electrostatic solitons in multispecies electron–positron plasmas. Astrophys. Space Sci. 239, 125–139 (1996)

    ADS  MATH  Google Scholar 

  • F. Verheest, M.A. Hellberg, I. Kourakis, Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons. Phys. Rev. E 87(4), 043107 (2013a)

    ADS  Google Scholar 

  • F. Verheest, M.A. Hellberg, I. Kourakis, Electrostatic supersolitons in three-species plasmas. Phys. Plasmas 20(1), 012302 (2013b)

    ADS  Google Scholar 

  • F. Verheest, M.A. Hellberg, I. Kourakis, Ion-acoustic supersolitons in plasmas with two-temperature electrons: Boltzmann and kappa distributions. Phys. Plasmas 20(8), 082309 (2013c)

    ADS  Google Scholar 

  • F. Verheest, G.S. Lakhina, M.A. Hellberg, No electrostatic supersolitons in two-component plasmas. Phys. Plasmas 21(6), 062303 (2014)

    ADS  Google Scholar 

  • G.M. Webb, J.F. McKenzie, E.M. Dubinin, K. Sauer, Hamiltonian formulation of nonlinear travelling Whistler waves. Nonlinear Process. Geophys. 12, 643–660 (2005)

    ADS  Google Scholar 

  • G.M. Webb, J.F. McKenzie, R.L. Mace, C.M. Ko, G.P. Zank, Dual variational principles for nonlinear traveling waves in multifluid plasmas. Phys. Plasmas 14(8), 082318 (2007)

    ADS  Google Scholar 

  • G.M. Webb, C.M. Ko, R.L. Mace, J.F. McKenzie, G.P. Zank, Integrable, oblique travelling waves in quasi-charge-neutral two-fluid plasmas. Nonlinear Process. Geophys. 15, 179–208 (2008)

    ADS  Google Scholar 

  • G.M. Webb, R.H. Burrows, X. Ao, G.P. Zank, Ion acoustic traveling waves. J. Plasma Phys. 80, 147–171 (2014)

    ADS  Google Scholar 

  • G.M. Webb, J.F. McKenzie, G.P. Zank, Multi-symplectic magnetohydrodynamics: II, addendum and erratum. J. Plasma Phys. 81(6), 905810610 (2015)

    Google Scholar 

  • M.Y. Yu, H. Luo, A note on the multispecies model for identical particles. Phys. Plasmas 15(2), 024504 (2008)

    ADS  Google Scholar 

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Acknowledgements

The authors are grateful to Prof. Valery Nakariakov and Prof. George Rowlands for valuable discussions and constructive comments. D.Y. Kolotkov acknowledges the support of the STFC consolidated grant ST/L000733/1. A. E. Dubinov worked in the framework of the Program of Increasing the Competitiveness of NRNU MEPhI.

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Authors and Affiliations

  1. Sarov Institute for Physics and Technology, Sarov, Nizhniy Novgorod Region, Russia, 607188

    Alexander E. Dubinov

  2. National Research Nuclear University “MEPhI”, Moscow, Russia, 115409

    Alexander E. Dubinov

  3. Department of Physics, Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, UK

    Dmitrii Y. Kolotkov

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  1. Alexander E. Dubinov
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  2. Dmitrii Y. Kolotkov
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Correspondence to Dmitrii Y. Kolotkov.

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Dubinov, A.E., Kolotkov, D.Y. Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas. Rev. Mod. Plasma Phys. 2, 2 (2018). https://doi.org/10.1007/s41614-018-0014-9

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