A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations

Yueh Cheng Kuo, Wen-Wei Lin, Shih Feng Shieh, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We aim at developing methods to track minimal energy solutions of time-independent m-component coupled discrete nonlinear Schrödinger (DNLS) equations. We first propose a method to find energy minimizers of the 1-component DNLS equation and use it as the initial point of the m-component DNLS equations in a continuation scheme. We then show that the change of local optimality occurs only at the bifurcation points. The fact leads to a minimal energy tracking method that guides the choice of bifurcation branch corresponding to the minimal energy solution curve. By combining all these techniques with a parameter-switching scheme, we successfully compute a non-radially symmetric energy minimizer that can not be computed by existing numerical schemes straightforwardly.

Original languageEnglish
Pages (from-to)7941-7956
Number of pages16
JournalJournal of Computational Physics
Volume228
Issue number21
DOIs
StatePublished - 20 Nov 2009

Keywords

  • Continuation method
  • Coupled nonlinear Schrödinger equations
  • Ground states
  • Minimal energy
  • Non-radially symmetric solutions

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