Existence and linearized stability of solitary waves for a quasilinear Benney system

2014/03/02 by João‐Paulo Dias, João-Paulo Dias, Mário Figueira +4
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1403.0199

arxiv created 2014/03/02 · openalex publication_date 2014/03/02 · arxiv updated 2014/03/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove the existence of solitary wave solutions to the quasilinear Benney system iu_t+u_xx=a|u|^pu+uv, v_t+f(v)_x=(|u|²)_x where f(v)=-γv³, -1<p<+∞ and a,γ>0. We establish, in particular, the existence of travelling waves with speed arbitrary large if p<0 and arbitrary close to 0 if p>\frac 23. We also show the existence of standing waves in the case -1<p≤ \frac 23, with compact support if -1<p<0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.

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