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

Bona, J. L.; Souganidis, P. E.; Strauss, W. A.

Proc. R. Soc. Lond., Ser. A 411, 395-412 (1987).

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

MSC:

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

Keywords:

stability analysis; solitary wave solutions; Korteweg-de Vries type nonlinear evolution equation; sufficient condition; solitary waves; non- convexity; energy functional

Citations:

Zbl 0617.35072