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The (2 + 1)-dimensional modified Kadomtsev-Petviashvili equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of Lax pairs. Abel-Jacobi coordinates are introduced to straighten the flows, from which quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation are obtained in terms of Riemann theta functions.
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Geng et al. (1999) studied this question.
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