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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Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Wiley
2020-01-01
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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. |
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ISSN: | 2314-8896 2314-8888 |