Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems
Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems
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由 Neumann 型系统产生的耦合修正 Kadomtsev-Petviashvili 方程的一些代数几何解
DOI：
10.1063/1.4736838
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发表时间：
2012-07
影响因子：
1.3
通讯作者：
Chen Jinbing
中科院分区：
文献类型：
--
作者：
Chen Jinbing
利用Neumann型系统，通过三个步骤给出了耦合修正Kadomtsev-Petviashvili（cmKP）方程和一族1+1维可积非线性发展方程（INLEE）的代数几何解的处理方法：（i）根据Lax对的非线性化，将cmKP方程和1+1维INLEE约化为辛子流形上的一族相容Neumann型系统，其对合解在2+1维和1+1维上都给出了INLEE的有限参数解;（ii）从Riemman曲面的超椭圆曲线上的全纯微分和Abel映射出发，引入Abel-Jacobi变量来理顺Neumann型流，（iii）基于Riemann定理和迹公式，对拉直流进行Jacobi反演，得到了cmKP方程的新的代数几何解和1+1维可积族.
A treatment is described for getting some algebro-geometric solutions of the coupled modified Kadomtsev-Petviashvili (cmKP) equations and a hierarchy of 1+1 dimensional integrable nonlinear evolution equations (INLEEs) by using the Neumann type systems through three steps: (i) according to the nonlinearization of Lax pair, the cmKP equations and the 1+1 dimensional INLEEs are reduced to a family of compatible Neumann type systems on a symplectic submanifold, whose involutive solutions give rise to the finite parametric solutions of the INLEEs in both 2+1 and 1+1 dimensions; (ii) from the holomorphic differentials and the Abel map on a hyperelliptic curve of Riemman surface, the Abel-Jacobi variables are introduced to straighten out the Neumann type flows, the 1+1 and 2+1 dimensional flows giving the Abel-Jacobi solutions; (iii) based on the Riemann theorem and the trace formulas, the Jacobi inversion is applied to the straightened flows for getting some new algebro-geometric solutions of the cmKP equations and the 1+1 dimensional integrable hierarchy.
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影响因子：
8.6
作者：
E. Tracy;H. H. Chen-H.;Y. C. Lee
通讯作者：
E. Tracy;H. H. Chen-H.;Y. C. Lee
影响因子：
2.4
作者：
Evgeny Sklyanin
通讯作者：
Evgeny Sklyanin
影响因子：
2.4
作者：
M. Alber;R. Camassa;Yuri N. Fedorov;Darryl D. Holm;J. Marsden
通讯作者：
M. Alber;R. Camassa;Yuri N. Fedorov;Darryl D. Holm;J. Marsden
影响因子：
1.3
作者：
Jinbing Chen
通讯作者：
Jinbing Chen
影响因子：
1.3
作者：
Ruguang Zhou
通讯作者：
Ruguang Zhou