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arXiv · 1902.02876

Nonlinear interactions between solitons and dispersive shocks in focusing media

Gino Biondini·Jonathan Lottes
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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.

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Gino Biondini, Jonathan Lottes. 2019-02-16. Nonlinear interactions between solitons and dispersive shocks in focusing media. https://doi.org/10.1103/physreve.99.022215

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