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Focusing and multi-focusing solutions of the nonlinear Schrödinger equation. (English) Zbl 0694.35196

Summary: A method of dynamic rescaling of variables is used to investigate numerically the nature of the focusing singularities of the cubic and quintic Schrödinger equations in two and three dimensions and describe their universal properties. The same method is applied to simulate the multi-focusing phenomena produced by simple models of saturating nonlinearities.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B99 Qualitative properties of solutions to partial differential equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
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