Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations - Journal of Applied Mathematics and Physics

JAMP > Vol.9 No.12, December 2021

Journal of Applied Mathematics and Physics

Volume 9, Issue 12 (December 2021)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations ()

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DOI: 10.4236/jamp.2021.912206 141 Downloads 781 Views Citations

Author(s)

Yifan Liu¹, Guojiang Wu^2*

Affiliation(s)

¹United Christian Academy, Civic Center Drive, Rancho Cucamonga, USA.
²Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, China.

ABSTRACT

In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As m → 0 and m → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics.

KEYWORDS

Auxiliary Equation Method, Nonlinear Evolution Equations, Periodic Wave Solutions, Mapping Method, Solitary Wave Solutions

Share and Cite:

Liu, Y. and Wu, G. (2021) Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations. Journal of Applied Mathematics and Physics, 9, 3155-3164. doi: 10.4236/jamp.2021.912206.

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