| Camassa-Holm方程凹凸尖峰及光滑孤立子解 |
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| 引用本文： | 田立新,许刚,刘曾荣.Camassa-Holm方程凹凸尖峰及光滑孤立子解[J].应用数学和力学,2002,23(5):497-506. |
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| 作者姓名： | 田立新 许刚 刘曾荣 |
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| 作者单位： | 1. 江苏理工大学,数学系,江苏,镇江,212013
2. 上海大学,数学系,上海,200018 |
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| 基金项目： | 国家自然科学基金资助 (10 0 710 331)，江苏省自然科学基金资助 (BQ980 2 3)，教育部骨干教师基金资助 (2 0 0 0 65_30 ) |
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| 摘 要： | 研究一类完全可积的新型浅水波方程Camassa-Holm方程的行波孤立子解及双孤立子解。引入凹凸尖峰孤立子光滑孤立子的概念，研究得到该方程的行波解中具有尖峰性质的凹凸尖峰孤立子解及光滑孤立子解。同时利用Backlund变换给出该类方程的新的双孤立子解。
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| 关 键 词： | 孤立子 可积系统 行波解 浅水波方程 Camassa－Holm方程 光滑孤立子解 |
| 文章编号： | 1000-0887(2002)05-0497-10 |
| 修稿时间： | 2001年8月20日 |
The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation |
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| TIAN Li_xin ,XU Gang ,LIU Zeng_rong.The Concave or Convex Peaked and Smooth Soliton Solutions of Camassa-Holm Equation[J].Applied Mathematics and Mechanics,2002,23(5):497-506. |
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| Authors: | TIAN Li_xin XU Gang LIU Zeng_rong |
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| Institution: | TIAN Li_xin 1,XU Gang 1,LIU Zeng_rong 2 |
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| Abstract: | The traveling wave soliton solutions and pair soliton solution to a class of new completely integralbe 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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| Keywords: | soliton peakson integrable system traveling wave solution |
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