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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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 |
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| 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: | 01 Aug 2021 11:21 |
| URI: | http://nrl.northumbria.ac.uk/id/eprint/30858 |
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