关键词: 非线性发展方程 , 直接代数方法 , 假设方法 , 精确解 , 孤波解 , 周期波解.

Abstract:

Some explicit and exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluidu\-t+a\-0u\-x+a\-1uu\-x+a\-2u\-\{xxx\}+b\-0u\-\{xx\}+b\-1(uu\-x)\-x+b\-2u\-\{xxx x\}=0are obtained by a kind of combiantion of the direct algebraic method and the ansatze method. These solutions include three travelling solitary wave solutions, singular travelling wave solutions and periodic wave solutions of triangular function type. Some results of other papers can be regard as a special case of the result in this paper. Futhermore, some new special solutions of the equation are obtained and some mistakes and careless of other paper are corrected.

Key words: Nonlinear evolution equation, Direct algebraic method , Ansatze methord, Exact solutions, Sollitary wave solutions, Periodic wave solution