Non-self-similar collapsing solutions of the nonlinear Schrödinger equation at the critical dimension
- 1 August 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 48 (2), R684-R687
- https://doi.org/10.1103/physreve.48.r684
Abstract
The dynamical problem of a spherically symmetric wave collapse is investigated in the framework of the nonlinear Schrödinger equation defined at the critical dimension. Collapsing solutions are shown to remain self-similar for spatial coordinates below a cutoff radius only, and to exhibit at larger distances a non-self-similar tail whose expression is explicitly computed. A rapid method used to study the time behavior and the stability of the contraction rate associated with these singular solutions is also derived.Keywords
This publication has 14 references indexed in Scilit:
- Computer simulation of wave collapses in the nonlinear Schrödinger equationPhysica D: Nonlinear Phenomena, 1991
- The interaction representation in the self-focusing theoryPhysica D: Nonlinear Phenomena, 1991
- Dynamics of wave collapse in the critical casePhysics Letters A, 1990
- Langmuir wave collapse with anisotropic contraction ratesPhysical Review A, 1990
- Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimensionPhysical Review A, 1988
- Local structure of the self-focusing singularity of the nonlinear Schrödinger equationPhysica D: Nonlinear Phenomena, 1988
- Focusing and multi-focusing solutions of the nonlinear Schrödinger equationPhysica D: Nonlinear Phenomena, 1988
- Blow-up in Nonlinear Schroedinger Equations-I A General ReviewPhysica Scripta, 1986
- Blow-up in Nonlinear Schroedinger Equations-II Similarity structure of the blow-up singularityPhysica Scripta, 1986
- Self-Trapping of Optical BeamsPhysical Review Letters, 1964