一类非线性非局部扰动LGH方程的孤子行波解  

Soliton Travelling Wave Solutions to a Class of Nonlinear Nonlocal Disturbed LGH Equations

作　　者：冯依虎[1,2] 莫嘉琪[2] 

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《应用数学和力学》2016年第4期426-433,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(40676016);安徽省教育厅自然科学基金(KJ2015A347);安徽省高校优秀青年人才支持重点项目(gxyq ZD2016520)~~

摘　　要：利用经过改进的泛函分析变分迭代方法讨论了一类非线性非局部Landau-Ginzburg-Higgs(LGH)微分方程.首先,做行波变换,引入泛函,并求出其变分,令其为0,得到了Lagrange(拉格朗日)算子应满足的条件,并求出它.然后,引入一个经过改进的变分迭代式,选取初始迭代函数为对应的无扰动LGH方程的孤子解.最后,利用迭代式依次得到非线性非局部LGH扰动方程求出各次孤子行波的渐近解和LGH扰动方程的精确解.通过一个例子说明了用经过改进的泛函分析变分迭代方法得到求解是有效的方法.A class of nonlinear nonlocal Landau-Ginzburg-Higgs （LGH） differential equations were discussed with the modified functional analytic variational iteration method. Firstly, a set of travelling wave transforms were constructed and the functional was introduced, of which the variation was determined and then was made equal to 0 to obtain the conditions for and solution of the Lagrange operator. Secondly, a modified variational iteration expression was employed and the soliton solutions to the corresponding non-disturbed LGH equations were selected as the initial iteration functions. Finally, all the asymptotic solutions and the exact solutions to the nonlinear noniocal disturbed LGH equations were obtained, successively. From an example, the proposed modified functional analytic variational iteration method is proved valid and practica- ble.

关 键 词：行波 非线性 非局部 

分 类 号：O175.29[理学—数学]