Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation |
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Authors: | Gegenhasi Ya-Qian Li Duo-Duo Zhang |
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Institution: | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China |
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Abstract: | In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. |
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Keywords: | modified differential-difference KP equation source generation procedure determinant solution Bäcklund transformation |
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