Stability and instability of solitary waves of Korteweg-de Vries type. (English) Zbl 0648.76005

The authors provide a stability analysis for solitary wave solutions of a Korteweg-de Vries type nonlinear evolution equation. The main result of the paper is a necessary and sufficient condition for stability (or instability) of solitary waves according to the convexity or non- convexity of a certain energy functional of the wave solutions as a function of the speed of the waves. This criterium was first given by J. Shatah in the analysis of the stability of ground states of nonlinear evolution equations [e.g.: Trans. Am. Math. Soc. 290, 701-710 (1985; Zbl 0617.35072)].
Reviewer: H.Lange


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
35Q99 Partial differential equations of mathematical physics and other areas of application


Zbl 0617.35072
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