A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation

Mark Ablowitz, Yi-Ping Ma, Igor Rumanov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
21 Downloads (Pure)


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 languageEnglish
Pages (from-to)1248-1268
JournalSIAM Journal on Applied Mathematics
Issue number4
Early online date17 Aug 2017
Publication statusE-pub ahead of print - 17 Aug 2017


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