Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application

The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to b...

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Bibliographic Details
Main Authors: Xiao-Feng Yang, Yi Wei
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/4912159
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Summary:The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. The KdV equation, Burgers equation, Boussinesq equation, and Sawada-Kotera equation are chosen to illustrate the validity of our method. We find that the underlying relation among the G′/G-expansion method, Hirota’s method, and HB method is a bilinear equation. The proposed method is also a standard and computable method, which can be generalized to deal with other types of NLPDE.
ISSN:2314-8896
2314-8888