Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

[2] David C., Sagaut P., Spurious solitons and structural stability of finite differ- ence schemes for nonlinear wave equations, under press for Chaos, Solitons and Fractals.

A canonical variable for the spatial Dysthe equation for the wave envelope u has been identified by means of the gauge transformation (6), and the hidden Hamilto- nian structure

Let us mention that our results only apply to the solitary wave solutions which we obtain from the solitary waves of the nonlinear Schrödinger equation in the nonrelativistic limit

Based on the well-known Mountain Pass Lemma due to Ambrosetti and Rabinowitz, we will show in Theorem 3.18 and Theorem 3.19 that if κ is suitably large, then among all nonzero

The rest of the paper is divided as follows. In Section 2, we gather some useful facts about scalar nonlinear Schr¨odinger equations and their solitary waves. Then in Section 3 we

One of the first existence result of multi-solitons for non-integrable equations was obtained by Merle [34] as a by-product of the construction of a multiple blow-up points solution

Using the exact solitary wave solution (2.20) we can assess the accuracy of the Serre equations (with β = 1 3 ) by making comparisons with corresponding solutions to the original

In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawa- hara equation (gKW) which is a fifth order dispersive equation.. For some values of