Some new soliton solutions for the nonlinear the fifth-order integrable equations

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

3 Department of Mathematics, University of Bonab, Bonab, Iran.

Abstract

‎In this work‎, ‎we established some exact solutions for the‎ $(1+1)$-dimensional and $(2+1)$-dimensional fifth-order integrable‎ equations ($(1+1)$D and $(2+1)$D FOIEs) which is considered based on‎ the improved $\tanh(\phi(\xi)/2)$ expansion method (IThEM)‎, ‎by‎ utilizing Maple software‎. ‎We obtained new periodic solitary wave‎ ‎solutions‎. ‎The obtained solutions include soliton‎, ‎periodic‎, ‎kink‎, kink-singular wave solutions‎. ‎Comparing our new results with Wazwaz‎ results‎, ‎namely‎, ‎the Hereman-Nuseri method shows that our results give‎ further solutions‎. ‎Many other such types of nonlinear equations‎ arise in fluid dynamics‎, ‎plasma ‎physics,‎ and nonlinear physics‎.

Keywords

References

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Computational Methods for Differential Equations
Volume 10, Issue 2
April 2022
Pages 445-460

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History

  • Receive Date: 10 December 2018
  • Revise Date: 17 December 2020
  • Accept Date: 24 December 2020

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