Solitary-wave solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order

摘要

In this Letter, based on the idea of Adomian's decomposition method and with help of Mathematica, we obtain the exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. In this paper by considering the decomposition scheme, we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy is finally demonstrated in the study of some values p⩾1 of the compound KdV-type and compound KdV–Burgers-type equations.