B?CKLUND TRANSFORMATION TO SOLVE THE GENERALIZED (3+1)-DIMENSIONAL KP-YTSF EQUATION AND KINKY PERIODIC-WAVE, WRONSKIAN AND GRAMMIAN SOLUTIONS

The Kadomtsev-Petviashvili equation is considered to be a basic model describing nonlinear dispersive wave in fluids, which is an integrable equation with two spatial dimensions. The Yu-To da-Sasa- Fukuyama equation plays a crucial role in fluid dynamics, plasma physics and weakly dispersive media. In this paper, we investigate a generalized (3+1)-dimensional KadomtsevPetviashvili-Yu-Toda-Sasa-Fukuyama equation, and multiple types of solutions are derived. With symbolic computation, a class of kinky periodic-wave solutions, determinant solutions and the bilinear Backlund transformation are constructed. We obtain two types of determinant solutions, that is, Wronskian and Grammian solutions. By choosing the appropriate matrix elements of determinants, many kinds of solutions are derived. In addition to the soliton solutions, the complexiton solutions and rational solutions are given. As illustrative examples, a few particular solutions are computed and plotted.