(2+1)维广义Nizhnik-Novikov-Veselov方程的几种类型新解及其相互作用  

Several Types of New Solutions and Interactions of the (2+1) Dimension Generalized Nizhnik-Novikov-Veselov Equation

作　　者：套格图桑[1,2,3] 伊丽娜 Taogetusang;YI Lina(College of Mathematics Science,Inner MongoliaNormal University,Hohhot 010022,China;Department of Mathematics.Hohhot University for Nationalities,Hohhot 010051,China;College o f Mathematical,Inner Mongolia Universit y for Nationalities,Tongliao 028043,China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]呼和浩特民族学院数学系,呼和浩特010051 [3]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《内蒙古大学学报（自然科学版）》2020年第6期561-568,共8页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11361040);内蒙古自治区自然科学基金(2020LH01008);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古民族大学科学研究基金资助项目(NMDGP1713)资助。

摘　　要：通过函数变换和符号计算系统Mathematica,获得了(2+1)维广义Nizhnik-Novikov-Veselov(N-N-V)方程的几种新结论。步骤1:给出函数变换,将(2+1)维广义N-N-V方程的求解问题转化为几个常微分方程和非线性代数方程组的求解问题。步骤2:借助符号计算系统Mathematica,求出非线性代数方程组的几组解。步骤3:在此基础上,构造(2+1)维广义N-N-V方程的三个任意函数组成的分离变量解和两个任意函数与常微分方程的解组成的分离变量解。步骤4:用符号计算系统Mathematica,分析解的相互作用。Several new conclusions of the(2+1)dimension generalized Nizhnik-Novikov-Veselov(N-N-V)equation are obtained by using the function transformation and symbol computing system Mathematica.Step1,give the function transformation,and transform the problem of solving solutions of the(2+1)dimension generalized N-N-V equation into the problem of solving solutions of several ordinary differential equations and nonlinear algebraic equations.Step 2,by using the symbolic computation system Mathematica,several sets of solutions of nonlinear algebraic equations are solved.Step3,on this basis,the separation variables solutions composed of three arbitrary functions and the separation variables solutions composed of two arbitrary functions and the solutions of the ordinary differential equation of the(2+1)dimension generalized N-N-V equation are constructed.Step4,use the symbolic computation system Mathematica to analyze and understand the interaction of the solutions.

关 键 词：函数变换 (2+1)维广义Nizhnik-Novikov-Veselov方程 分离变量解 解的相互作用 

分 类 号：O175.14[理学—数学]