浅水长波近似方程组的多孤波解、有理分式解

Multi-solitary Wave Solutions and Rational Fraction Solutions for the Approximate Equations for Long Waves in Shallow Water

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。

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.