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.
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机译：Instruction on the construction of coherent structures based on variable separation solutions of (2+1)-dimensional nonlinear evolution equations in fluid mechanics
