Linear stability of shock waves for the Schrodinger-Burgers system

Details Linear stability of shock waves for the Schrodinger-Burgers system Linear stability of shock waves for the Schrodinger-Burgers system

2012-02-27

arxiv.org/abs/1202.5837v2

Mathematics

Analysis of PDEs

19 pages

Scientific paper

We investigate a system coupling the nonlinear Schrodinger equation and the inviscid Burgers equation, which models interactions between short and long waves (for instance in fluids). Well-posedness for the associated Cauchy problem remains a difficult open problem and so we tackle it here via a linearization technique. We establish a linearized stability theorem for the Schrodinger-Burgers system when the reference solution is an entropy-satisfying shock wave to Burgers equation. Our proof is based on suitable energy estimates and on properties of hyperbolic equations with discontinuous coefficients. Numerical experiments support and expand our theoretical results.

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