Exact periodic cross-kink wave solutions for the (2+1)-dimensional Korteweg-de Vries equation

The movement of any object has a certain natural law, and the studies and solutions to many natural laws boil down to the problem of mathematical physics equations. Many important physical situations such as fluid flows, plasma physics, and solid state physics have been described by the Korteweg-de Vries (KdV)-type models. In this article, the (2+1)-dimensional KdV equation is presented. By using the Hirota's bilinear form and the extended Ansatz function method, we obtain new exact periodic cross-kink wave solutions for the (2+1)-dimensional KdV equation. With the aid of symbolic computation, the properties for these exact periodic cross-kink wave solutions are shown with some figures.