A Universal Asymptotic Regime in the Hyperbolic Nonlinear Schrödinger Equation

Abstract

The appearance of a fundamental long-time asymptotic regime in the two space-one time dimensional hyperbolic nonlinear Schrödinger (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 a wide range of initial data.