EXACT 1ST-ORDER SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION
EXACT 1ST-ORDER SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION
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DOI：
10.1007/bf01017105
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发表时间：
1987-08-01
影响因子：
1
通讯作者：
KULAGIN, NE
中科院分区：
文献类型：
--
作者：
AKHMEDIEV, NN;ELEONSKII, VM;KULAGIN, NE
提出了一种求非线性薛定谔方程精确解的方法。它使用一个未知函数的真实的和虚部由一个线性关系连接的系数，只依赖于时间的一个anatomy。该方法包括构造一个常微分方程组，其解确定非线性薛定谔方程的解。所得到的解决方案，形成一个三参数的家庭，可以表示在椭圆雅可比函数和第三类不完全椭圆积分。在一般情况下，所得到的解决方案是周期的空间变量和双周期的时间。特殊情况下的解决方案可以表示在椭圆雅可比函数和初等函数的详细考虑。的解决方案的实际应用的可能领域中提到的。
A method is proposed for finding exact solutions of the nonlinear Schr~ dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~ dinger equation. The obtained solutions form a three-parameter family that can be expressed in terms of elliptic Jacobi functions and the incomplete elliptic integral of the third kind. In the general case, the obtained solutions are periodic with respect to the spatial variable and doubly periodic with respect to the time. Special cases for which the solutions can be expressed in terms of elliptic Jacobi functions and elementary functions are considered in detail. Possible fields of practical applications of the solutions are mentioned.