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arXiv · 1810.11504

Riemann problems and dispersive shocks in self-focusing media

Gino Biondini
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Abstract

The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions with a jump in either or both the amplitude and the local wavenumber are considered. It is shown analytically and numerically that the space-time plane divides into expanding domains in which the solution is described by a slow modulation of genus-zero, genus-one or genus-two solutions, their precise arrangement depending on the specifics of the initial datum

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Gino Biondini. 2018-10-26. Riemann problems and dispersive shocks in self-focusing media. https://doi.org/10.1103/physreve.98.052220

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