TY - JOUR

T1 - Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation

AU - Fibich, Gadi

AU - Levy, Doron

N1 - Funding Information:
We wish to thankA lexanderN epomniashchfyo r suggestingth is problema nd for usefuld iscussions. The researcho f D.L. was supportedb y TMR grant #ERBFMRXCT960033P. art of this work was done whilet hes econda uthorw asv isitingt heT el Aviv University,a visit which was supportedb y the Sackler Institutefo r ScientificC omputationast Tel Aviv University.

PY - 1998/12/7

Y1 - 1998/12/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038938431&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(98)00744-0

DO - 10.1016/S0375-9601(98)00744-0

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AN - SCOPUS:0038938431

SN - 0375-9601

VL - 249

SP - 286

EP - 294

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4

ER -