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The nonlocal symmetries for the modified Kadomtsev-Petviashvili (mKP)equation are obtained with the truncated Painleve method. The nonlocalsymmetries can be localized to the Lie point symmetries by introducingauxiliary dependent variables. The finite symmetry transformations andsimilarity reductions related with the nonlocal symmetries are computed. Themulti-solitary wave solution and interaction solutions among a soliton and thecnoidal waves of the mKP equation are presented. In the meanwhile, theconsistent tanh expansion (CTE) method is applied to the mKP equation. Theexplicit interaction solutions among a soliton and other types of nonlinearwaves such as the cnoidal periodic waves and multiple resonant solitonsolutions are given.

Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method