Application of an irrational trial equation method to high-dimensional nonlinear evolution equations. (English) Zbl 1253.35027

Summary: An analytic technique, an irrational trial equation method, is applied to solve the \((3+1)\)-dimensional potential-YTSF equation and the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equations. Using this method, some exact travelling wave solutions to two high-dimensional nonlinear evolution equations are obtained. This method provides us with a new way to obtain series solutions of such problems.


35C07 Traveling wave solutions
35P05 General topics in linear spectral theory for PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
35C10 Series solutions to PDEs