Self-Focusing in the Damped Nonlinear Schrödinger Equation
- 1 January 2001
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 61 (5) , 1680-1705
- https://doi.org/10.1137/s0036139999362609
Abstract
We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δth for the damping parameter δ such that when δ> δ th damping arrests blowup. When δ< δ th, the solution blows up at the same asymptotic rate as the undamped nonlinear Schrodinger equation.Keywords
This publication has 27 references indexed in Scilit:
- Self-focusing of elliptic beams: an example of the failure of the aberrationless approximationJournal of the Optical Society of America B, 2000
- Critical power for self-focusing in bulk media and in hollow waveguidesOptics Letters, 2000
- Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical DimensionSIAM Journal on Applied Mathematics, 1999
- Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equationPhysics Letters A, 1998
- A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equationPhysics Letters A, 1998
- Adiabatic law for self-focusing of optical beamsOptics Letters, 1996
- Small Beam Nonparaxiality Arrests Self-Focusing of Optical BeamsPhysical Review Letters, 1996
- Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equationPhysica D: Nonlinear Phenomena, 1992
- On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general caseJournal of Functional Analysis, 1979
- Computer Studies in Self-FocusingPhysical Review B, 1969