A perfectly matched layer approach to the nonlinear Schrödinger wave equations |
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| Institution: | 1. Department of Computational Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea;2. Department of Mechanical Engineering, Hanbat National University, Daejeon 34158, Republic of Korea;3. Department of Mechanical Engineering, Yonsei University, Seoul 03722, Republic of Korea;1. Department of Computational Mathematics, Science, and Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, MI 48824, USA;2. Department of Mechanical Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, MI 48824, USA;3. Division of Applied Mathematics, Brown University, 182 George, Providence, RI 02912, USA;1. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China;2. Department of Mathematics, and MOE–LSC, Shanghai Jiaotong University, Shanghai, 200240, China;1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, 119076, Singapore;2. State Key Lab of Power Systems and Department of Electrical Engineering, Tsinghua University, Beijing 100084, China;1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Absorbing boundary conditions (ABCs) are generally required for simulating waves in unbounded domains. As one of those approaches for designing ABCs, perfectly matched layer (PML) has achieved great success for both linear and nonlinear wave equations. In this paper we apply PML to the nonlinear Schrödinger wave equations. The idea involved is stimulated by the good performance of PML for the linear Schrödinger equation with constant potentials, together with the time-transverse invariant property held by the nonlinear Schrödinger wave equations. Numerical tests demonstrate the effectiveness of our PML approach for both nonlinear Schrödinger equations and some Schrödinger-coupled systems in each spatial dimension. |
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