New Variable Separation Solutions for Two Nonlinear Evolution Equations in Higher Dimensions

Based on the multi-linear variable separation approach, a new direct variable separation algorithm is proposed. The effectiveness of the algorithm is demonstrated by the applications of the (2+1)-dimensional modified Korteweg-de Vries equation and the (3+1)-dimensional BKP equation. The new variable separation solutions which include at least one arbitrary function are derived for these two equations with the aid of Maple.