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

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  • LeMesurier, Brenton J.

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.

Suggested Citation

  • LeMesurier, Brenton J., 2001. "Multi-focusing and sustained dissipation in the dissipative nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 503-517.
    • Handle: RePEc:eee:matcom:v:55:y:2001:i:4:p:503-517
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