中国物理B ›› 2013, Vol. 22 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/22/7/070201

• GENERAL •    下一篇

Multi-symplectic scheme for the coupled Schrödinger–Boussinesq equations

黄浪扬a, 焦艳东b, 梁德民c   

  1. a School of Mathematical Sciences, Huaqiao University, Quanzhou 362011, China;
    b School of Sciences, Hebei University of Technology, Tianjin 300401, China;
    c Department of Electronics, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
  • 收稿日期:2013-03-10 修回日期:2013-04-08 出版日期:2013-06-01 发布日期:2013-06-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11271171, 11001072, and 11101381), the Natural Science Foundation of Fujian Province, China (Grant No. 2011J01010), the Fundamental Research Funds for the Central Universities, China, and the National Science Foundation of Huaqiao University, China (Grant No. 10QZR21).

Multi-symplectic scheme for the coupled Schrödinger–Boussinesq equations

Huang Lang-Yang (黄浪扬)a, Jiao Yan-Dong (焦艳东)b, Liang De-Min (梁德民)c   

  1. a School of Mathematical Sciences, Huaqiao University, Quanzhou 362011, China;
    b School of Sciences, Hebei University of Technology, Tianjin 300401, China;
    c Department of Electronics, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China
  • Received:2013-03-10 Revised:2013-04-08 Online:2013-06-01 Published:2013-06-01
  • Contact: Huang Lang-Yang E-mail:hly6@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11271171, 11001072, and 11101381), the Natural Science Foundation of Fujian Province, China (Grant No. 2011J01010), the Fundamental Research Funds for the Central Universities, China, and the National Science Foundation of Huaqiao University, China (Grant No. 10QZR21).

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摘要： In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrödinger–Boussinesq equations (CSBE). Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.

关键词: coupled Schrö, dinger–, Boussinesq equations, multi-symplectic scheme, conservation laws, numerical experiments

Abstract: In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrödinger–Boussinesq equations (CSBE). Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.

Key words: coupled Schrödinger–Boussinesq equations, multi-symplectic scheme, conservation laws, numerical experiments

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.70.Bf (Finite-difference methods) 02.30.Jr (Partial differential equations)