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A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations |
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| Authors: | Yueh-Cheng Kuo Wen-Wei Lin Shih-Feng Shieh Weichung Wang |
| Affiliation: | aDepartment of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan;bDepartment of Applied Mathematics, National Chiao-Tung University, Hsinchu 300, Taiwan;cDepartment of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan;dDepartment of Mathematics, National Taiwan University, Taipei 106, Taiwan |
| 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. |
| Keywords: | Coupled nonlinear Schrö dinger equations Continuation method Ground states Minimal energy Non-radially symmetric solutions |
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