On dissipationless shock waves in a discrete nonlinear Schrödinger equation

Details On dissipationless shock waves in a discrete nonlinear Schrödinger equation On dissipationless shock waves in a discrete nonlinear Schrödinger equation

2003-06-30

arxiv.org/abs/nlin/0306061v1

Nonlinear Sciences

Pattern Formation and Solitons

15 pages, 9 figures

Scientific paper

It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.

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