A Note on Some Sub-Equation Methods and New Types of Exact Travelling Wave Solutions for Two Nonlinear Partial Differential Equations |
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Authors: | Huiqun Zhang |
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Institution: | (1) College of Mathematical Science, Qingdao University, Qingdao, Shandong, 266071, People’s Republic of China |
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Abstract: | Sub-equation methods are used for constructing exact travelling wave solutions of nonlinear partial differential equations.
The key idea of these methods is to take full advantage of all kinds of special solutions of sub-equation, which is usually
a nonlinear ordinary differential equation. We present a function transformation which not only gives us a clear relation
among these sub-equation methods, but also can be used to obtain the general solutions of these sub-equations. And then new
exact travelling wave solutions of the CKdV-MKdV equation and the CKdV equations as applications of this transformation are
obtained, and the approach presented in this paper can be also applied to other nonlinear partial differential equations.
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Keywords: | Exact travelling wave solutions General solutions Sub-equation methods CKdV-MKdV equation CKdV equations |
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