Algebro-Geometric Solution to the Modified Kadomtsev-Petviashvili Equation

The modified Kadomtsev–Petviashvili (mKP) equation is split into two soliton equations in the modified Jaulent–Miodek (mJM) hierarchy, and further into integrable finite-dimensional Hamiltonian systems (FDHSs) using the nonlinearization of Lax pairs. The Abel–Jacobi coordinate is introduced to linearize the mKP flow such that its solution is reduced as a linear superposition, expressed in the Abel–Jacobi variable. Finally, the algebro-geometric solution of the mKP equation is given via the Jacobi inversion.

[1]  Ruguang Zhou,et al.  The finite-band solution of the Jaulent–Miodek equation , 1997 .

[2]  A. Fordy,et al.  Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems , 1989 .

[3]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[4]  H. Dai,et al.  Decomposition of certain nonlinear evolution equations and their quasi-periodic solutions , 2002 .

[5]  Boris Konopelchenko,et al.  Some new integrable nonlinear evolution equations in 2 + 1 dimensions , 1984 .

[6]  Xianguo Geng,et al.  Relation between the Kadometsev–Petviashvili equation and the confocal involutive system , 1999 .

[7]  X. Geng,et al.  Classical Integrable Systems Generated Through Nonlinearization of Eigenvalue Problems , 1990 .

[8]  Vladimir E. Zakharov,et al.  A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I , 1974 .

[9]  S. Novikov,et al.  Theory of Solitons: The Inverse Scattering Method , 1984 .

[10]  Gui‐zhang Tu,et al.  The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems , 1989 .

[11]  Yi Cheng,et al.  The constraint of the Kadomtsev-Petviashvili equation and its special solutions , 1991 .

[12]  H. Dai,et al.  Algebro-geometric solutions of (2+1)-dimensional coupled modified Kadomtsev–Petviashvili equations , 2000 .

[13]  D. Mumford.  Tata Lectures on Theta I , 1982 .

[14]  Algebro-geometric solutions to a hierarchy of (1 + 1)-dimensional and two new (2 + 1)-dimensional nonlinear evolution equations , 2004 .

[15]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[16]  Joe W. Harris,et al.  Principles of Algebraic Geometry: Griffiths/Principles , 1994 .

[17]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .