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. ISSN 0036-1399 (In Press)

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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
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 26 May 2017 08:51
Last Modified: 26 May 2017 09:41
URI: http://nrl.northumbria.ac.uk/id/eprint/30858

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