Abstract: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.
殷久利, 田立新. 一类浅水波模型的可积性、守恒量和新型孤立波[J]. 江苏大学学报(自然科学版), 2009, 30(2): 213-216.
Yin Jiuli, Tian Lixin. Integrability,conservation laws and new solitary waves of one type of shallow water wave models[J]. Journal of Jiangsu University(Natural Science Eidtion)
, 2009, 30(2): 213-216.