A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation

Ablowitz, Mark, Ma, Yi-Ping and Rumanov, Igor (2017) A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation. SIAM Journal on Applied Mathematics, 77 (4). pp. 1248-1268. ISSN 0036-1399

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Official URL: https://doi.org/10.1137/16M1099960

Abstract

The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrodinger (HNLS) equation is discussed. Based on analytical and numerical simulations, a wide range of initial conditions corresponding to initial lumps of moderate energy are found to approach a quasi-self-similar solution. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling those of the self-similar solution, with appropriate small modifications. This solution has aspects that suggest it is a universal attractor emanating from wide ranges of initial data.

Item Type: Article
Uncontrolled Keywords: nonlinear waves, hyperbolic NLS equation, long-time asymptotics
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 26 May 2017 08:51
Last Modified: 22 Sep 2017 11:10
URI: http://nrl.northumbria.ac.uk/id/eprint/30858

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