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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (5): 557-567.

• 论文 • 上一篇    下一篇

THE CONCAVE OR CONVEX PEAKED AND SMOOTH SOLITON SOLUTIONS OF CAMASSA-HOLM EQUATION

田立新1, 许刚1, 刘曾荣2   

  1. 1. Department of Mathematics, Jiangsu University of Science and Technolgoy, Zhenjiang 212013, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200018, P. R. China
  • 收稿日期:2001-08-20 修回日期:2001-11-28 出版日期:2002-05-18 发布日期:2002-05-18
  • 基金资助:
    the National Natural Science Foundation of China(100710331);the Natural Science Foundation of Jiangsu(BQ98023);the Education Department Foundation for Backbone Teachers(200065-30)

THE CONCAVE OR CONVEX PEAKED AND SMOOTH SOLITON SOLUTIONS OF CAMASSA-HOLM EQUATION

TIAN Li-xin1, XU Gang1, LIU Zeng-rong 2   

  1. 1. Department of Mathematics, Jiangsu University of Science and Technolgoy, Zhenjiang 212013, P. R. China;
    2. Department of Mathematics, Shanghai University, Shanghai 200018, P. R. China
  • Received:2001-08-20 Revised:2001-11-28 Online:2002-05-18 Published:2002-05-18
  • Supported by:
    the National Natural Science Foundation of China(100710331);the Natural Science Foundation of Jiangsu(BQ98023);the Education Department Foundation for Backbone Teachers(200065-30)

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摘要： The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.

Abstract: The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.

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