Riemann problems and dispersive shocks in self-focusing media Article Swipe

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Genus Modulation (music) Jump Discontinuity (linguistics) Riemann surface Riemann hypothesis Nonlinear system Riemann problem Modulation space Mathematics Space (punctuation) Mathematical analysis Amplitude Physics Classical mechanics Optics Quantum mechanics Computer science Acoustics Botany Biology Operating system

Gino Biondini ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1103/physreve.98.052220 · OA: W2898300373

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