Long-time asymptotics of the nonlinear Schrödinger equation shock problem
Published
Journal Article
The long-time asymptotics of two colliding plane waves governed by the focusing nonlinear Schrödinger equation are analyzed via the inverse scattering method. We find three asymptotic regions in space-time: a region with the original wave modified by a phase perturbation, a residual region with a one-phase wave, and an intermediate transition region with a modulated two-phase wave. The leading-order terms for the three regions are computed with error estimates using the steepest-descent method for Riemann-Hilbert problems. The nondecaying initial data requires a new adaptation of this method. A new breaking mechanism involving a complex conjugate pair of branch points emerging from the real axis is observed between the residual and transition regions. Also, the effect of the collision is felt in the plane-wave state well beyond the shock front at large times. © 2007 Wiley Periodicals, Inc.
Full Text
Duke Authors
Cited Authors
- Buckingham, R; Venakides, S
Published Date
- September 1, 2007
Published In
Volume / Issue
- 60 / 9
Start / End Page
- 1349 - 1414
Electronic International Standard Serial Number (EISSN)
- 0010-3640
International Standard Serial Number (ISSN)
- 0010-3640
Digital Object Identifier (DOI)
- 10.1002/cpa.20179
Citation Source
- Scopus