古德曼函数及其在求解非线性演化方程中的应用  

Gudermann function and its application for solving nonlinear evolution equations

作　　者：石玉仁[1] 王雪玲[1] 王林雪[1] 宗谨[1] 杨红娟[1] 

机构地区：[1]西北师范大学物理与电子工程学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2015年第2期37-41,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11047010)

摘　　要：基于最小二乘法的思想基础,提出了一种用古德曼函数构造非线性演化方程孤立波解的半解析方法.以Burgers方程和KdV方程为例,发现该方法给出的孤波解与相应的精确解吻合得很好.该方法也可以推广到求解其他非线性演化方程的孤立波解.Based on the thought of the least square method,a semi-analytical method,in which the Gudermann function is applied,is presented for obtaining the solitary wave solutions of a class of nonlinear evolution equations.As an example,this method is applied to find the solitary wave solutions of the Burgers equation and the KdV equation.The solitary wave solutions are agreement well with the exact ones.The method presented in this paper can also be generalized to find the solitary wave solutions of a class of nonlinear evolution equations.

关 键 词：古德曼函数 最小二乘法 孤立波解 

分 类 号：O411.1[理学—理论物理]