Extended Tanh-Function Method and Its Applications in Nonlocal Complex mKdV Equations

Xiaodong Wang (), Jianping Wu, Yazi Wang and Can Chen ()
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Xiaodong Wang: School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
Jianping Wu: School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
Yazi Wang: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Can Chen: School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China

Mathematics, 2022, vol. 10, issue 18, 1-9

Abstract: In order to construct the multiple traveling wave solutions of the nonlocal modified Korteweg de Vires (mKdV) equation, the modified tanh-function approach for local soliton equations is extended to a nonlocal complex mKdV equation. The central idea of this method is to use the solution of the Riccati equation to replace the tanh function in the tanh function (THF) method. As an application, we investigate a new traveling wave solution for the nonlocal complex mKdV equation of Ablowitz and Musslimani. Moreover, some exciting diagrams show the underlying dynamics of some given solutions.

Keywords: nonlocal complex mKdV equation; extended tanh-funtion method; riccati equation; travelling wave solution; symbolic computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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