Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

DOI10.1137/S0036139902411855zbMath1032.65091MaRDI QIDQ4429804

Gadi Fibich, Boaz Ilan, Semyon V. Tsynkov

Publication date: 28 September 2003

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear Schrödinger equationlaser beamsingularity formationself-focusingnonlinear wave propagationbackscatteringnonlinear Helmholtz equationlinear dampingnonparaxialityKerr mediumlimiting absorptiontwo-way ABCs

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Diffraction, scattering (78A45) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Waves and radiation in optics and electromagnetic theory (78A40) Physical optics (78A10)

Related Items (5)

High-order numerical solution of the nonlinear Helmholtz equation with axial symmetry ⋮ Thermal effects in short laser pulses: suppression of wave collapse ⋮ A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension ⋮ An existence theorem for some semilinear elliptic systems ⋮ Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions

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