首次积分法求变系数(3+1)维非线性薛定谔方程的精确解  

The First Integral Method for the Exact Solution of the(3+1)Dimensional Nonlin⁃ear Schrodinger Equations with Variable Coefficients

作　　者：欧阳坦 肖冰[1] OUYANG Tan;XIAO Bing(College of Mathematical Sciences,Xinjiang Normal University,Urumqi,Xinjiang,830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《新疆师范大学学报（自然科学版）》2022年第1期16-21,共6页Journal of Xinjiang Normal University(Natural Sciences Edition)

摘　　要：文章运用首次积分方法求解一个变系数的(3+1)维非线性薛定谔方程的精确解,以前常用的方法为达朗贝尔解的结构理论,即先求其对应齐次方程的通解,再求非齐次方程的一个特解,但此方法在解非线性问题中难度较大。首次积分方法是冯兆生在求解非线性偏微分方程时提出的有效积分方法,该方法应用交换代数的理论,通过引入行波变换,将非线性偏微分方程转换成常微分方程,再根据多项式除法定理,得到非线性偏微分方程的精确解。The first integral method is used to solve the exact solution of a(3+1)dimensional nonlinear Schro-dinger equation with variable coefficients.In the past,we used the structure theory of D'Alembert solution,that is,to solve the general solution of the corresponding homogeneous equation,and then to find a particular solution of the non-homogeneous equation,but this method is difficult to solve nonlinear problems.The first integral method is an effective integral method proposed by Feng Zhao-sheng when solving nonlinear partial differential equations.This method uses the theory of commutative algebra to transform nonlinear partial differential equations into ordinary dif-ferential equations by introducing traveling wave transformation,and then obtains the exact solution of nonlinear par-tial differential equations according to the polynomial division theorem.

关 键 词：首次积分法 (3+1)维非线性薛定谔方程 偏微分方程 

分 类 号：O175.14[理学—数学]