基于首次积分法求解两个非线性薛定谔方程的精确解
The First Integral Method for Solving Exact Solutions of Two Nonlinear Schrodinger Equations
摘要: 首次积分方法是由冯第一个提出的对非线性偏微分方程进行可靠处理的积分方法，该方法是基于交换代数环的理论。本文将利用首次积分法对广义非线性薛定谔方程和高阶色散非线性薛定谔方程的精确行波解进行研究。即先通过引入恰当的行波变换，将非线性薛定谔方程化为常微分方程，再根据多项式除法原理，得到两个非线性薛定谔方程的精确行波解。
Abstract: The first integral method proposed by Feng is very reliable integral method for solving nonlinear partial differential equations, which is based on the ring theory of commutative algebra. In this paper, exact travelling wave solutions of the generalized nonlinear Schrodinger equation and the high order dispersion nonlinear Schrodinger equation are studied by using the first integral me-thod. By introducing the travelling wave transformations, two nonlinear Schrodinger equations have been transformed into ordinary differential equations. Then according to the division theorem of polynomial, exact travelling wave solutions of two nonlinear Schrodinger equations are obtained.
文章引用：张清梅, 熊梅, 陈龙伟. 基于首次积分法求解两个非线性薛定谔方程的精确解[J]. 应用数学进展, 2018, 7(7): 962-969. https://doi.org/10.12677/AAM.2018.77113

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