On integrability of nonautonomous nonlinear schrödinger equations

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

Original languageEnglish (US)
Pages (from-to)3067-3082
Number of pages16
JournalProceedings of the American Mathematical Society
Volume140
Issue number9
DOIs
StatePublished - Sep 1 2012

Keywords

  • Completely integrable systems
  • Generalized harmonic oscillators
  • Green's function
  • Lax pair
  • Nonlinear Schrödinger equations
  • Propagator
  • Zakharov-Shabat system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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