A nonlinear model describing a short wave long wave interaction in a viscoelastic medium
Analysis of PDEs
2012-02-07 v1
Abstract
In this paper we introduce a system coupling a nonlinear Schr\"odinger equation with a system of viscoelasticity, modeling the interaction between short and long waves, acting for instance on media like plasmas or polymers. We prove the existence and uniqueness of local (in time) strong solutions and the existence of global weak solutions for the corresponding Cauchy problem. In particular we extend previous results in [Nohel \emph{et. al.}, Commun. Part. Diff. Eq., 13 (1988)] for the quasilinear system of viscoelasticity. We finish with some numerical computations to illustrate our results.
Cite
@article{arxiv.1202.1235,
title = {A nonlinear model describing a short wave long wave interaction in a viscoelastic medium},
author = {Paulo Amorim and João-Paulo Dias},
journal= {arXiv preprint arXiv:1202.1235},
year = {2012}
}