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

Amorim, Paulo; Dias, João

doi:10.1090/S0033-569X-2012-01298-4

Authors: Paulo Amorim and João Paulo Dias
Journal: Quart. Appl. Math. 71 (2013), 417-432
MSC (2010): Primary 35M31
DOI: https://doi.org/10.1090/S0033-569X-2012-01298-4
Published electronically: October 1, 2012
MathSciNet review: 3112821
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Abstract: 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 instance on media such as 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 et. al., Commun. Part. Diff. Eq., 13 (1988)] for the quasilinear system of viscoelasticity. We finish with some numerical computations to illustrate our results.

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