直接拟解法求Boussinesq方程组的精确解  

Exact Solution for Solving Boussinesq Equations by Using Direct Quasi Solution

作　　者：李伟[1] 李丽[1] LI Wei;LI Li(College of Mathematics and Physics,Bohai University,Jinzhou,Liaoning Province,121013 China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《科技资讯》2021年第30期166-168,共3页Science & Technology Information

基　　金：国家自然科学基金资助项目(项目编号:61603055)。

摘　　要：微分方程包含常微分方程和偏微分方程。由于非线性偏微分方程是偏微分方程的重要内容,求微分方程的解是微分方程研究的重要内容,从而求非线性偏微分方程的解是微分方程研究内容中的重中之重。很多重大的物理科学问题和信息技术问题都与非线性偏微分方程的研究紧密相关。一般来说,求非线性偏微分方程的解是不容易的。经过科研工作者不断努力已经找到了大量的求解方法。该文借助于行波变换法,直接拟解法和齐次法解得了Boussinesq的新解。这种方法也具有一定的普遍性,可以求一些非线性偏微分方程的解。Differential equations include ordinary differential equations and partial differential equations.Because nonlinear partial differential equation is an important content of partial differential equation,the solution of differential equation is the important content of differential equation research,so the solution of nonlinear partial differential equation is the most important content of differential equation research.Many important physical science and information technology problems are closely related to the study of nonlinear partial differential equations.Generally speaking,it is not easy to find the solution of nonlinear partial differential equations.Through the continuous efforts of scientific researchers,a large number of solutions have been found.In this paper,a new solution of Boussinesq is obtained by means of Traveling Wave Transformation method,Direct Quasi solution and Homogeneous solution.This method also has certain universality,and can find the solutions of some nonlinear partial differential equations.

关 键 词：行波变换 精确解 拟解 齐次平衡法 

分 类 号：O175.2[理学—数学]