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The modified Kadomtsev–Petviashvili (mKP) equation is revisited from two 1 + 1-dimensional integrable equations whose compatible solutions yield a special solution of the mKP equation in view of a transformation. By employing the finite-order expansion of Lax matrix, the mKP equation is reduced to three solvable ordinary differential equations (ODEs). The associated flows induced by the mKP equation are linearized under the Abel–Jacobi coordinates on a Riemann surface. Finally, a finite band solution expressed by Riemann-theta functions for the mKP equation is obtained through the Jacobi inversion.

Decomposition of the Modified Kadomtsev–Petviashvili Equation and its Finite Band Solution