DECOMPOSITION OF THE MODIFIED KADOMTSEV–PETVIASHVILI EQUATION AND ITS FINITE BAND SOLUTION
DECOMPOSITION OF THE MODIFIED KADOMTSEV–PETVIASHVILI EQUATION AND ITS FINITE BAND SOLUTION
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DOI：
10.1142/s1402925111001428
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发表时间：
2011-01
影响因子：
0.7
通讯作者：
Jinbing Chen;Z. Qiao
中科院分区：
文献类型：
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作者：
Jinbing Chen;Z. Qiao
从两个1 + 1维可积方程出发，重新讨论了修正的Kadomtsev-Petviashvili（mKP）方程，其相容解通过变换得到了mKP方程的特解.利用Lax矩阵的有限阶展开，将mKP方程化为三个可解的常微分方程.由mKP方程诱导的关联流在Riemann曲面上的Abel-Jacobi坐标下线性化。最后，通过Jacobi反演得到了mKP方程的Riemann-theta函数表示的有限带解.
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.