中国物理B ›› 2004, Vol. 13 ›› Issue (7): 984-987.doi: 10.1088/1009-1963/13/7/002

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The soliton-like solutions to the (2+1)-dimensional modified dispersive water-wave system

张鸿庆1, 李德生2   

  1. (1)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; (2)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; Science School, Shenyang University of Technology, Shenyang 110023, China
  • 收稿日期:2003-10-28 修回日期:2004-02-27 出版日期:2004-07-05 发布日期:2005-07-05
  • 基金资助:
    Project supported by the National Key Basic Research Special Foundation of China (Grant No 1998030600) and the National Natural Science Foundation of China (Grant No 10072013).

The soliton-like solutions to the (2+1)-dimensional modified dispersive water-wave system

Li De-Sheng (李德生)ab, Zhang Hong-Qing (张鸿庆)a   

  1. a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Science School, Shenyang University of Technology, Shenyang 110023, China
  • Received:2003-10-28 Revised:2004-02-27 Online:2004-07-05 Published:2005-07-05
  • Supported by:
    Project supported by the National Key Basic Research Special Foundation of China (Grant No 1998030600) and the National Natural Science Foundation of China (Grant No 10072013).

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摘要： By a simple transformation, we reduce the (2+1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.

关键词: (2+1)-dimensional modified dispersive water-wave system, generalized tanh-function method, soliton-like solutions

Abstract: By a simple transformation, we reduce the (2+1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method.

Key words: (2+1)-dimensional modified dispersive water-wave system, generalized tanh-function method, soliton-like solutions

中图分类号:  (Partial differential equations)

  • 02.30.Jr
03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 02.30.Hq (Ordinary differential equations) 45.05.+x (General theory of classical mechanics of discrete systems)