一类浅水波模型的可积性、守恒量和新型孤立波

Integrability,conservation laws and new solitary waves of one type of shallow water wave models

分析一类浅水波模型即广义CH方程中对流项强度及系数对可积性和显式解结构的影响.通过Painleve分析,证明m=2时方程是可积的,并且给出其守恒量和Ham ilton结构.推广一种统一的代数求解方法,把平衡关系式的变量数增加到3个,从而获得广义CH方程更为丰富的显式解,特别是一些新型孤波解:当m=1时,方程具有移动紧孤立波解(对流项系数为负号)以及移动尖峰孤立波解(对流项系数为正号);当m=2时,可积方程具有光滑孤立波解和周期波解;当m=3时方程具有周期波解.

Influence of intensity and coefficients of convections on the integrability and structure of exact solutions for one type of shallow water wave models,namely the generalized CH equation is analyzed.Through the Painleve analysis,it is proved that the equation is integrable as m=2,and conservation laws and Hamilton structure are also given.One unified algebra solution method is extended by changing the balance relationship variable number to three,and hence richer explicit solutions are obtained.Some new solitary wave solutions are： for m=1,the equation permits shifting compact solitary wave solutions when the convection coefficient is negative,and shifting peak solitary wave solutions when the convection coefficient is positive;for m=2,the equation permits the smooth solitary wave solution and the periodic wave solutions;for m=3,the equation has the periodic wave solutions.