TY - JOUR

T1 - A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation

AU - Fibich, Gadi

AU - Papanicolaou, George

PY - 1998/3/2

Y1 - 1998/3/2

N2 - In this Letter we introduce a systematic perturbation method for analyzing the effect of small perturbations on critical self-focusing by reducing the perturbed critical nonlinear Schrödinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simplified depending on whether PNLS is power conserving or not. An important and somewhat surprising result is that various small defocusing perturbations lead to a canonical form for the modulation equations, whose solutions have slowly decaying focusing-defocusing oscillations.

AB - In this Letter we introduce a systematic perturbation method for analyzing the effect of small perturbations on critical self-focusing by reducing the perturbed critical nonlinear Schrödinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simplified depending on whether PNLS is power conserving or not. An important and somewhat surprising result is that various small defocusing perturbations lead to a canonical form for the modulation equations, whose solutions have slowly decaying focusing-defocusing oscillations.

KW - Modulation theory

KW - Nonlinear Schrödinger equation

KW - Self-focusing

UR - http://www.scopus.com/inward/record.url?scp=0000256483&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(97)00941-9

DO - 10.1016/S0375-9601(97)00941-9

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AN - SCOPUS:0000256483

SN - 0375-9601

VL - 239

SP - 167

EP - 173

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

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

IS - 3

ER -