Explicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV-Burgers-type equations with nonlinear terms of any order

摘要

In this paper, we have improved the tanh-method by means of a proper transformation and a general ansatz. Applying the improved method and direct assumption method with symbolic computation, we consider two kinds of equations, general two-dimensional KdV-type equations with nonlinear terms of any order, (u(t) + au(p)u(x) + bu(2p)u(x) + deltau(xxx))(x) + su(yy) = 0, and general two-dimensional KdV-Burgers-type equations with nonlinear terms of any order, (u(t) + au(p)u(x) + bu(2p)u(x) + gammau(xx) + deltau(xxx))(x) + su(yy) = 0. As a result, rich explicit exact solutions for these two equations, which contain kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, rational solutions, periodic solutions and combined formal solutions, are obtained. [References: 22]