Appication of Symbolic Computation in the Variable-Coefficient mKP Equation

In this paper, based on symbolic computation, we apply the Pfaffianization procedure of Ohta and Hirota to the variable-coefficient mKP (vcmKP) equation. We first present the N-soliton solutions in terms of Grammian determinant by employing the bilinear formalism . Then by applying the method of Pfaffianization to the vcmKP case, we derive the bilinear form of the Pfaffianized vcmKP equation. Finally by the dependent variable transformation, a new integrable, coupled vcmKP system in nonlinear form is derived. To our knowledge, the procedure of Pfaffianization has not been extended to the non-isospectral and variable-coefficient equations before. We expect that this Pfaffianization technique is applicable to other non-isospectral and variable-coefficient integrable equations which admit determinant solutions.