Multi-focusing and sustained dissipation in the dissipative nonlinear Schrödinger equation

Brenton J. LeMesurier

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 55, issue 4, 503-517

Abstract: The possibility of physically relevant singular solutions of the nonlinear Schrödinger equation with sustained dissipation into the singularity is considered through numerical study of a nonlinear dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, including the two-dimensional case of laser self-focusing, involving a multi-focusing mechanism. The space and time structure of such solutions for very small values of the nonlinear dissipation parameter is studied numerically and compared to a conjectured mechanism related to a new family of stationary singular solutions of the NLSE.

Keywords: Nonlinear Schrödinger equation; Dissipative; Nonlinear (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:55:y:2001:i:4:p:503-517

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