非线性演化方程孤立波的同伦分析法求解  

Solving solitary wave solutions of nonlinear evolution equations with the homotopy analysis method

作　　者：杨红娟[1] 石玉仁[1] 段文山[1] 吕克璞[1] 

机构地区：[1]西北师范大学物理与电子工程学院,兰州730070

出　　处：《物理学报》2007年第6期3064-3069,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10247008)资助的课题~~

摘　　要：利用同伦分析法求解了Burgers方程,得到了其扭结形孤立波的近似解析解,该解非常接近于相应的精确解.结果表明,同伦分析法可用来求解非线性演化方程的孤立波解.同时,也对所用方法进行了一定扩展,得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解.We solved the Burgers equation by using the homotopy analysis method （HAM） and obtained its approximate kink solitary wave solutions. The solutions agree very well with the exact solutions. The results indicate that the HAM is valid for finding the solitary wave solutions of a class of nonlinear evolution equations. We also made some efforts to extend the HAM. As an example, we got the bell-like solitary wave solutions of KP equation by this approach. Our extended method can be used to find the approximate solitary wave solutions for more nonlinear evolution equations in an easy way.

关 键 词：BURGERS方程 同伦分析法 KP方程 孤立波解 

分 类 号：O175.29[理学—数学]