A hyperplane-constrained continuation method for near singularity in coupled nonlinear Schrödinger equations

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The continuation method is a useful numerical tool for solving differential equations to obtain multiform solutions and allow bifurcation analysis. However, when a standard continuation method is used to solve a type of time-independent m-coupled nonlinear Schrödinger (NLS) equations that can be used to model nonlinear optics, nearly singular systems arise in the computations of prediction and correction search directions and detections of bifurcations. To overcome the stability and efficiency problems that exist in standard continuation methods, we propose a new hyperplane-constrained continuation method by adding additional constraints to prevent the singularities while tracking the solution curves. Aimed at the 3-coupled DNLS equations, we conduct theoretical analysis to the solutions and bifurcations on the primal stalk solution curve. The proposed algorithms have been implemented successfully to demonstrate numerical solution profiles, energies, and bifurcation diagrams in various settings.

Original languageEnglish
Pages (from-to)513-526
Number of pages14
JournalApplied Numerical Mathematics
Volume60
Issue number5
DOIs
Publication statusPublished - 2010 May 1

Keywords

  • Bifurcation analysis
  • Coupled nonlinear Schrödinger equations
  • Hyperplane-constrained continuation method
  • Numerical solutions
  • Primal stalk solutions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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