聚焦非线性薛定谔方程超椭圆解的有效积分
Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation
摘要：
基于Jacobi反演问题的经典解，利用Kleinian超椭圆函数，提出了一种求解聚焦非线性薛定谔方程拟周期两相解的有效积分方法.已知具有实拟周期的两相解形成二维环面，模复相位因子的圆，其可以表示为theta函数的比率。在本文中，两相解决方案的显式参数化的分支点的亏格2黎曼曲面的theta函数。简单的公式，在分支点的虚部，得到的最大模和最小模的两相溶液。
英文摘要：
An effective integration method based on the classical solution to the Jacobi inversion problem, using Kleinian ultra-elliptic functions, is presented for quasi-periodic two-phase solutions of the focusing nonlinear Schrödinger equation. The two-phase solutions with real quasi-periods are known to form a two-dimensional torus, modulo a circle of complex phase factors, that can be expressed as a ratio of theta functions. In this paper, the two-phase solutions are explicitly parametrized in terms of the branch points on the genus-two Riemann surface of the theta functions. Simple formulas, in terms of the imaginary parts of the branch points, are obtained for the maximum modulus and the minimum modulus of the two-phase solution.
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