中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3628-3631.doi: 10.1088/1674-1056/18/9/004

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The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation

林苏榕1, 莫嘉琪2   

  1. (1)Department of Computer, Fujian Radio and TV University, Fuzhou 350003, China; (2)Department of Mathematics, Anhui Normal University, Wuhu 241000, China;Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China;Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240, China
  • 收稿日期:2008-06-16 修回日期:2008-10-16 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010), the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08), LASG State Key Laboratory Special fund and E-Institutes of Shanghai Municipal Education Commission of China (Grant No E03004).

The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation

Mo Jia-Qi(莫嘉琪)a)b)c)† and Lin Su-Rong(林苏榕)d)   

  1. a Department of Mathematics, Anhui Normal University, Wuhu 241000, China; b Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Chinac Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240, Chinad Department of Computer, Fujian Radio and TV University, Fuzhou 350003, China
  • Received:2008-06-16 Revised:2008-10-16 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010), the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08), LASG State Key Laboratory Special fund and E-Institutes of Shanghai Municipal Education Commission of China (Grant No E03004).

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摘要： This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy.

Abstract: This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy.

Key words: evolution equation, nonlinear, soliton, approximate method

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations)