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Inverse Spectral Transform for the Modified Kadomtsev‐Petviashvili Equation

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The 2 + 1‐modified Kadomtsev‐Petviashvili (mKP) equation is studied by the inverse‐spectral‐transform method. The initial‐value problems for the mKP‐1 and mKP‐11 equations are solved by the nonlocal Riemann‐Hilbert and techniques for initial data decaying sufficiently rapidly at infinity. The lump solutions for the mKP‐I equation are found explicitly. Wide classes of the exact solutions for the mKP equation—namely, the rational solutions, including the plane lumps for the mKP‐I equation; solutions with functional parameters; the plane solitons; and breathers—are constructed by the use of the method based on the nonlocal . The Miura transformation between the mKP and KP equations is discussed.
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Document Type: Research Article

Publication date: April 1, 1992

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