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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 $\left(3+1\right)$-dimensional potential-YTSF equation and the $\left(2+1\right)$-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.
##### MSC:
 35C07 Traveling wave solutions of PDE 35P05 General topics in linear spectral theory of PDE 35Q53 KdV-like (Korteweg-de Vries) equations 35C05 Solutions of PDE in closed form 35C10 Series solutions of PDE