Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains |
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| Affiliation: | 1. School of Science, Xuchang University, Xuchang 461000, China;2. Jiangsu Key Laboratory for NSLSCS, Jiangsu Collaborative Innovation Center of Biomedial Functional Materials, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;1. Department of Mathematics, Near East University, Mersin 10, TRNC, Turkey;2. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey;3. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar, PC 44891-63157 Vajargah, Iran;4. Department of Mathematics, Sonari College, Sonari 785690, Assam, India;5. Department of Mathematics, Barnagar College, Sorbhog 781317, Assam, India;1. UEB, Université Européenne de Bretagne, Université de Rennes 1, France;2. CNRS UMR 6082 FOTON, Enssat, 6 rue de Kerampont, CS 80518, 22305 Lannion, France;3. IRMAR, Université de Rennes I, CNRS, Campus de Beaulieu, 35042 Rennes, France;1. Octav Mayer Institute of Mathematics (Romanian Academy) and Al.I. Cuza University, 700506, Iaşi, Romania;2. Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany;3. Department of Mathematics, Shanghai Jiao Tong University, 200240 Shanghai, China |
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| Abstract: | The numerical simulation of coupled nonlinear Schrödinger equations on unbounded domains is considered in this paper. By using the operator splitting technique, the original problem is decomposed into linear and nonlinear subproblems in a small time step. The linear subproblem turns out to be two decoupled linear Schrödinger equations on unbounded domains, where artificial boundaries are introduced to truncate the unbounded physical domains into finite ones. Local absorbing boundary conditions are imposed on the artificial boundaries. On the other hand, the coupled nonlinear subproblem is an ODE system, which can be solved exactly. To demonstrate the effectiveness of our method, some comparisons in terms of accuracy and computational cost are made between the PML approach and our method in numerical examples. |
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