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广义高维Klein-Gordon强迫扰动方程的孤子解
引用本文:韩祥临,汪维刚,莫嘉琪.广义高维Klein-Gordon强迫扰动方程的孤子解[J].高校应用数学学报(A辑),2019,34(2):165-172.
作者姓名:韩祥临  汪维刚  莫嘉琪
作者单位:湖州师范学院 求真学院,浙江湖州,313000;合肥幼儿师范高等专科学校,安徽合肥,2300112;安徽师范大学 数学与统计学院,安徽芜湖,241003
基金项目:国家自然科学基金;浙江省自然科学基金;安徽省教育厅自然科学研究重点项目;安徽省教育厅自然科学研究重点项目;安徽省教育科学规划课题
摘    要:利用同伦映射方法研究了一类非线性广义强迫扰动Klein-Gordon方程.首先利用双曲正切待定系数法求得了无扰动项典型方程的孤子解.然后利用同伦映射原理得到了强迫扰动Klein-Gordon方程的任意次近似孤子解.最后叙述了得到的近似孤子解是一个解析展开式,还能对它进行解析运算.这对使用简单的模拟方法得到的近似解是达不到的.

关 键 词:孤子  非线性  KLEIN-GORDON方程

The solution of soliton to generalized higher dimensions Klein-Gordon forced disturbed equation
HAN Xiang-lin,WANG Wei-gang,MO Jia-qi.The solution of soliton to generalized higher dimensions Klein-Gordon forced disturbed equation[J].Applied Mathematics A Journal of Chinese Universities,2019,34(2):165-172.
Authors:HAN Xiang-lin  WANG Wei-gang  MO Jia-qi
Institution:(Qiuzhen School,Huzhou Teachers College,Huzhou 313000,China;Department of Basic,Hefei Preschool Education College,Hefei 230011,China;School of Mathematics&Statistics Science,Anhui Normal University,Wuhu 241003,China)
Abstract:A class of nonlinear generalized forced disturbed Klein-Gordon equation is considered by using the homotopic mapping method. Firstly, an approximate solution of soliton to typical nonlinear equation is solved using the method of undetermined coefficients for the hyperbolic tangent functions. Then, the approximate solution of soliton to nonlinear forced disturbed equation is obtained using the homotopic mapping principle. Finally, it is point out that the approximate solution of soliton is an analytic expression, so we can carry on analytic operation to it. But these can not obtain for the simple simulate method.
Keywords:soliton  nonlinear  Klein-Gordon equation
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