The homogeneous balance of undetermined coefficients method and its application

Open Mathematics

Yang Xiao-Feng¹  Wei Yi²  He Xin-Dang³ 

[1] College of Science, Northwest A&F University, Yangling 712100, Shaanxi, China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China;School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, China;

关键词: homogeneous balance of undetermined coefficients method;    bilinear equation;    eckhaus equation;    kdv equation;    generalized boussinesq equation;    35q55;    35q80;    35g25;   

DOI  :  10.1515/math-2016-0078

来源: DOAJ

【 摘 要 】

The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.

【 授权许可】

Unknown