Nonlinear interactions between solitons and dispersive shocks in focusing media

Abstract

Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel from a region with nonzero background towards a region with zero background, they always pass through the shock structure without generating dispersive radiation. However, their properties (such as amplitude, velocity and shape) change in the process. A similar effect arises when solitons travel from a region with zero background towards a region with nonzero background, except that, depending on its initial velocity, in this case the soliton may remain trapped inside the shock-like structure indefinitely. In all cases, the new soliton properties can be determined analytically. The results are validated by comparison with numerical simulations.

arXiv comment6 pages, 3 figures, to appear in Physical Review E

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• On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks