(2+1)维Camassa-Holm方程的相似约化与解析解

Similarity reductions and analytic solutions for the (2+1)-dimensional Camassa-Holm equations

将Clarkson和Krushal引入的直接约化方法推广并应用到 (2 +1)维Camassa Holm方程组 ,获得了该方程的若干相似约化和解析解 ,其中包括Logistic方程和Bernoulli方程 .约化结果得到了Peakon解、Cuspon解和关于时间t的奇异解 .

In this paper, the direct method proposed by Clarkson and Kruskal (CK) is extended and applied to the (2+1) dimensional Camassa Holm equations. As a result, several types of similarity reductions and analytic solutions are obtained, which contain Riccati equation, Logistic equation, Peakon solution, Cuspon solution and singularity solutions of t. The CK method can be applied to other nonlinear physics models.