Title: A hyperplane-constrained continuation method for near singularity in coupled nonlinear Schrodinger equations
Authors: Kuo, Yueh-Cheng
Lin, Wen-Wei
Shieh, Shih-Feng
Wang, Weichung
Department of Applied Mathematics
Keywords: Hyperplane-constrained continuation method;Coupled nonlinear Schrodinger equations;Numerical solutions;Primal stalk solutions;Bifurcation analysis
Issue Date: 1-May-2010
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 Schrodinger (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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.apnum.2009.11.007
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2009.11.007
Volume: 60
Issue: 5
Begin Page: 513
End Page: 526
Appears in Collections:Articles

Files in This Item:

  1. 000278220100001.pdf