Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation

Gadi Fibich, Doron Levy

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze self-focusing and singularity formation in the complex Ginzburg-Landau equation (CGL) in the regime where it is close to the critical nonlinear Schrödinger equation. Using modulation theory [Fibich and Papanicolaou, Phys. Lett. A 239 (1998) 167], we derive a reduced system of ordinary differential equations that describes self-focusing in CGL. Analysis of the reduced system shows that in the physical regime of the parameters there is no blowup in CGL. Rather, the solution focuses once and then defocuses. The validity of the analysis is verified by comparison of numerical solutions of CGL with those of the reduced system.

Original languageEnglish
Pages (from-to)286-294
Number of pages9
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume249
Issue number4
DOIs
StatePublished - 7 Dec 1998

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