Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations

Y. A. Li, K. Promislow

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We consider the linear stability and structural stability of non-ground state traveling waves of a pair of coupled nonlinear Schrödinger equations (CNLS) which describe the evolution of co-propagating polarized pulses in the presence of birefringence. Viewing the CNLS equations as a Hamiltonian perturbation of the Manakov equations, we find parameter regimes in which there are two stable families of traveling waves. The usual variational methods for stability analysis of ground states do not apply. Instead we employ a Liapunov-Schmidt type reduction to detect eigenvalues bifurcating from the imaginary axis. We also demonstrate the instability of a family of vector solitons.

Original languageEnglish
Pages (from-to)137-165
Number of pages29
JournalPhysica D: Nonlinear Phenomena
Volume124
Issue number1-3
DOIs
StatePublished - 1998

Keywords

  • Hamiltonian perturbation
  • Liapunov-Schmidt reduction
  • Non-ground states
  • Structural stability
  • Traveling waves

Fingerprint

Dive into the research topics of 'Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations'. Together they form a unique fingerprint.

Cite this