Abstract
The special features of the distribution of the magnetic field in the photosphere of the Sun and the experimental discovery of waves which propagate along magnetic tubes in the solar atmosphere have brought about the publication recently of a large number of articles which study the wave-conducting properties of media with a magnetic structure. One of the simplest cases was that of a plane magnetic layer, which was studied in detail in the linear approximation [1–3]. Starting from the dispersion properties of such a structure, [4] indicates the possibility of the existence in it of solitons in the approximation of waves of low amplitude which are long in relation to the layer. The present study has used the method of different-scale expansions to obtain the Schrödinger equation describing the propagation of nonlinear modulations of a symmetric harmonic mode over a plane magnetic layer in an incompressible fluid. A similar equation has been deduced, for example, for waves in water [5–9].
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Literature cited
B. Roberts, “Wave propagation in magnetically structured atmosphere. No. 2: Waves in a magnetic slab,” Sol. Phys.,69, 39 (1981).
P. M. Edwin and B. Roberts, “Wave propagation in magnetically structured atmosphcsre. No. 3. The slab in a magnetic environment,” Sol. Phys.,76, 239 (1982).
B. B. Chakraborty, “The hydromagnetic stability of a two-dimensional compressible jet,” Prog. Theor. Phys.,40, 210 (1968).
B. Roberts and A. Mangeney, “Solitons in solar magnetic flux tubes,” Mon. Not. R. Astron. Soc., 198, 7P (1982).
H. Hasimoto and H. Ono, “Nonlinear modulation of gravity waves,” J. Phys. Soc. Jpn.,33, 805 (1972).
A. Davey, “The propagation of a weak nonlinear wave,” J. Fluid Mech.,53, 769 (1972).
M. Tanaka, “Nonlinear self-modulation of interfacial waves,” J. Phys. Soc. Jpn.,51, 2016 (1982).
M. Tanaka, “Nonlinear self-modulation problem of the Benjamin-Ono equation,” J. Phys. Soc. Jpn.,51, 2686 (1982).
V. E. Zakharov, “The stability of periodic waves of finite amplitude on the surface of a deep fluid,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 86 (1968).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 164–168, March–April, 1985.
The author wishes to thank M. S. Ruderman for formulating the problem and for useful discussions, and V. B. Baranov for his attention to the study.
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Merzlyakov, E.G. Nonlinear long wave modulation in symmetric waves of a plane magnetic layer. Fluid Dyn 20, 305–309 (1985). https://doi.org/10.1007/BF01091047
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DOI: https://doi.org/10.1007/BF01091047