| 浅水长波近似方程组的多孤波解、有理分式解 |
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| 引用本文： | 聂小兵,贺秀霞.浅水长波近似方程组的多孤波解、有理分式解[J].华东师范大学学报(自然科学版),2002(2):15-21. |
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| 作者姓名： | 聂小兵 贺秀霞 |
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| 作者单位： | 华东师范大学,数学系,上海,200062 |
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| 基金项目： | 上海市重点学科建设基金 (2 0 0 1年 ) |
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| 摘 要： | 使用王明亮引进的齐次平衡法，求出了浅水长波近似方程组的Backlund变换以及它与热传导方程和二阶线性方程之间的Darboux变换，并借助于这些变换，获得了浅水长波近似方程组的多孤波解、有理分式解。推广了王明亮等人的结果。
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| 关 键 词： | 齐次平衡法 浅水长波近似方程组 Backlund变换 Darboux变换 多孤波解 有理分式解 |
| 文章编号： | 1000-5641(2002)02-0015-07 |
| 修稿时间： | 2000年11月1日 |
Multi-solitary Wave Solutions and Rational Fraction Solutions for the Approximate Equations for Long Waves in Shallow Water |
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| NIE Xiao bing,HE Xiu xia.Multi-solitary Wave Solutions and Rational Fraction Solutions for the Approximate Equations for Long Waves in Shallow Water[J].Journal of East China Normal University(Natural Science),2002(2):15-21. |
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| Authors: | NIE Xiao bing HE Xiu xia |
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| Abstract: | By using the homogeneous balance method, Backlund transformation of the approximate equations for long waves in shallow water is obtained, and Darboux transformations between the equation and the heat equation as well as linear equation of second order are derived. By means of the transformations, multi solitary wave solutions, rational fration solutions for the equation are found. The results obtained by professor Wang Mingliang and his partners are extended. |
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| Keywords: | homogeneous balance method approximate equations for long wave in shallow water Backlund transformation Darboux transformation multi solitary wave solution rational fraction solution |
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