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

✍ Scribed by Yueh-Cheng Kuo; Wen-Wei Lin; Shih-Feng Shieh; Weichung Wang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 742 KB
• Volume: 228
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2009.07.029

✦ Synopsis

We aim at developing methods to track minimal energy solutions of time-independent mcomponent 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.