Dissipation at singularities of the nonlinear Schrödinger equation through limits of regularisations

DOI10.1016/S0167-2789(99)00198-0zbMath0953.35132MaRDI QIDQ1581767

Brenton J. LeMesurier

Publication date: 8 October 2000

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

numerical resultsdissipationnonlinear Schrödinger equationsingularitymulti-focusing mechanismnumerical study of a dissipative regularisation

Mathematics Subject Classification ID

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) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)

Related Items (5)

Localizing estimates of the support of solutions of some nonlinear Schrödinger equations -- the stationary case ⋮ Regularization and control of self-focusing in the 2D cubic Schrödinger equation by attractive linear potentials ⋮ Multi-focusing and sustained dissipation in the dissipative nonlinear Schrödinger equation ⋮ Linear versus nonlinear dissipation for critical NLS equation ⋮ On a nonlinear Schrödinger equation with a localizing effect

Cites Work

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• Stability of isotropic singularities for the nonlinear Schrödinger equation
• Focusing and multi-focusing solutions of the nonlinear Schrödinger equation
• Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
• Isolated singularities in semilinear problems
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations

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