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.
Original language | English |
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Pages (from-to) | 1248-1268 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 77 |
Issue number | 4 |
Early online date | 17 Aug 2017 |
DOIs | |
Publication status | E-pub ahead of print - 17 Aug 2017 |
Keywords
- nonlinear waves
- hyperbolic NLS equation
- long-time asymptotics