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Explicit exact solitary-wave solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order. (English) Zbl 1028.35133
Summary: The authors consider compound KdV-type and KdV-Burgers-type equations with nonlinear terms of any order. The explicit exact solitary-wave solutions for the equations are obtained by means of proper transformation, which degrades the order of nonlinear terms, and an undetermined coefficient method. A solitary-wave solution with negative velocity for the generalized KdV-Burgers equation u t +u p u x -αu xx +u xxx =0 is found.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations