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 -