Example of shock wave in unstaible medium: The focusing nonlinear Schrodinger equation

Abstract

Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact solution of the Whitham-NS system, which ''partially saturates'' the modulational instability.

arXiv comment4 pages, LaTEX, version 2.09, submitted to Phys. Lett. A

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