João‐Paulo Dias

collaborators

2 papers

math.AP2014

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

João-Paulo Dias, Mário Figueira, Filipe Oliveira

We prove the existence of solitary wave solutions to the quasilinear Benney system $i u_{t} + u_{xx} = a ∣ u ∣^{p} u + uv, v_{t} + f (v)_{x} = (∣ u ∣^{2})_{x}$ where $f (v) = - γ v^{3}$ , $- 1 < p < + \infty$ and $a…

math.AP2012

A nonlinear model describing a short wave long wave interaction in a viscoelastic medium

Paulo Amorim, João-Paulo Dias

In this paper we introduce a system coupling a nonlinear Schrödinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for in…