非线性偏微分方程的行波解
Traveling wave solutions of nonlinear partial differential equations
摘要：
我们提出了一个简单的代数方法产生类的行波解决方案的各种偏微分方程的当前感兴趣的非线性科学。这个过程同样适用于可能或可能不可积的方程。我们用两种不同的模型来说明该方法，一种是由Rosenau-Hyman，Rosenau-Pikovsky和Rosenau-Hyman-Staley方程启发的一类模型中的包含峰的解决方案，另一种是由Camassa-Holm，Degasperis-Procesi和Dullin-Gotwald-Holm方程概括的系统中的包含峰的解决方案。在这两种情况下，我们得到新的类的解决方案之前没有研究过。
英文摘要：
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or may not be integrable. We illustrate the method with two distinct classes of models, one with solutions including compactons in a class of models inspired by the Rosenau-Hyman, Rosenau-Pikovsky and Rosenau-Hyman-Staley equations, and the other with solutions including peakons in a system which generalizes the Camassa-Holm, Degasperis-Procesi and Dullin-Gotwald-Holm equations. In both cases, we obtain new classes of solutions not studied before.
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