Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application. (28th April 2020)

• Record Type: Journal Article
• Authors: Yang, Xiao-Feng; Wei, Yi
• Other Names: Wang Liguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-04-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/4912159
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.