Abstract
We prove stability and instability theorems for solitary-wave solutions of classical scalar field equations.
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Lax, P. D.: Comm. Pure Appl. Math.21, 467 (1968)
Coleman, S.: Classical lumps and their quantum descendants. Lectures at the 1975 International School of Subnuclear Physics “Ettore Majorana” (Erice), in “New Phenomena in Subnuclear Physics,” Zichichi A. (ed.). New York: Plenum Press, 1977
Hepp, K.: Comm. Math. Phys.35, 265 (1974)
Benjamin, T. B.: Proc. R. Soc. (London)A328, 153 (1972)
Bona, J. L.: Proc. R. Soc. (London)A344, 363 (1975)
Scharf, G., Wreszinski, W. F.: Ann. Phys. (N.Y.)134, 56 (1981)
Derrick, G.: J. Math. Phys.5, 1252 (1964)
Strauss, W.: Nonlinear invariant wave equations. In: Invariant Wave Equations, Velo, G., Wightman, A. S. (eds.), Berlin, Heidelberg, New York: Springer 1977
Dunford, N., Schwartz, J.: Linear operators, Vol. II. New York: Interscience 1963
Martin, R. H.: Nonlinear operators and differential equations in Banach spaces. New York: Wiley 1976
Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. IV. New York: Academic Press 1978
Parenti, C., Strocchi, F., Velo, G.: In: Invariant Wave Equations, Velo, G., Wightman, A. S.: (eds.), Berlin, Heidelberg, New York: Springer 1977, and Commun. Math. Phys.53, 65 (1977)
Parenti, C., Strocchi, F., Velo, G.: Dynamical charges and symmetries in non-linear classical field theory. Bielefeld Preprint
Chernoff, P. R., Marsden, J. E.: properties of infinite dimensional Hamiltonian systems. Berlin, Heidelberg, New York: Springer 1974
Marsden, J., McCracken, M.: The Hopf bifurcation and its applications. Berlin, Heidelberg, New York: Springer 1976
Henry, Daniel B.: Stability and instability by the linear approximation, Proc. of the 12th. Brazilian Analysis Seminar (Soc. Bras. de Matematica, Rio de Janeiro)
Strauss, W. A.: Commun. Math. Phys.55, 149 (1977)
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Communicated by J. Moser
Partial financial support by FAPESP and FINEP.
Partial financial support by CNPq.
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Henry, D.B., Perez, J.F. & Wreszinski, W.F. Stability theory for solitary-wave solutions of scalar field equations. Commun.Math. Phys. 85, 351–361 (1982). https://doi.org/10.1007/BF01208719
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DOI: https://doi.org/10.1007/BF01208719