Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations
Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations
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DOI：
10.1088/0305-4470/36/9/307
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发表时间：
2003-02
期刊：
影响因子：
--
通讯作者：
X. Geng
中科院分区：
文献类型：
--
作者：
X. Geng
利用(1+1)维AKNS方程，将已知的(2+1)维破裂孤子方程、三势耦合KP方程和一个新的(3+1)维非线性发展方程分解为可解的常微分方程组。引入Abel-Jacobi坐标拉直伴随流，并用Riemann theta函数显式地给出了(2+1)维破裂孤子方程、耦合KP方程和(3+1)维发展方程的代数几何解。
The known (2+1)-dimensional breaking soliton equation, the coupled KP equation with three potentials and a new (3+1)-dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the (1+1)-dimensional AKNS equations. The Abel–Jacobi coordinates are introduced to straighten out the associated flows, from which algebraic-geometrical solutions of the (2+1)-dimensional breaking soliton equation, the coupled KP equation and the (3+1)-dimensional evolution equation are explicitly given in terms of the Riemann theta functions.