化归思想方法在偏微分方程求解中的应用  

Application of the transformation method in solving partial differential equations

作　　者：朱能 郑方韬 阮小军[1] ZHU Neng;ZHENG Fangtao;RUAN Xiaojun(Department of Mathematics,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《高师理科学刊》2020年第12期68-71,共4页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(11901277);江西省自然科学基金项目(20192BAB211004);南昌大学教学改革研究项目(NCUJGLX-2020-166-59)。

摘　　要：化归思想方法是偏微分方程求解的一种重要途径.以经典KdV方程求解为例,通过行波变换、极限转化和数值模拟验证,探讨化归思想方法在求解KdV方程孤立子中的应用.旨在提升学生对化归思想方法的掌握,丰富学生的解题技巧,培养学生的创新思维和应用实践能力.The transformation method is an important way to solve partial differential equations.Taking the solution of the classical KdV equation as examples,through the traveling wave transformation,limit process and numerical simulation,the application of the transformation method to solve the soliton of the KdV equation is discussed.It aims to improve the students′mastery of the thinking method of transformation,enrich their problem solving skills,and cultivate their innovative thinking and practical ability.

关 键 词：偏微分方程 孤立子 化归思想方法 

分 类 号：O175.2∶G642.0[理学—数学]