Open AccessSolving solitary wave solutions of nonlinear evolution equations with the homotopy analysis method
Author(s) -
Yang Hong-Juan,
Shi Yu-Ren,
Wen-Shan Duan,
Lü Ke-Pu
Publication year - 2007
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.56.3064
Subject(s) - homotopy analysis method , nonlinear system , homotopy perturbation method , traveling wave , burgers' equation , homotopy , class (philosophy) , physics , mathematical analysis , wave equation , mathematics , computer science , pure mathematics , quantum mechanics , artificial intelligence
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.