International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 6, Issue 8 (August 2019), Pages: 53-64

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 Original Research Paper

 Title: Applications of He's semi-inverse variational method and ITEM to the nonlinear long-short wave interaction system

 Author(s): Ramin Mehdizad Tekiyeh 1, Jalil Manafian 2, *, Haci Mehmet Baskonus 3, Faruk Düşünceli 4

 Affiliation(s):

 1Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
 3Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey
 4Faculty of Architecture and Engineering, Mardin Artuklu University, Mardin, Turkey

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0001-7201-6667

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2019.08.008

 Abstract:

This work deals with exact soliton solutions of the nonlinear long-short wave interaction system, utilizing two analytical methods. The system of coupled long-short wave interaction equations is studied by two analytical methods, namely, the generalized tan (ϕ/2)-expansion method and He’s semi-inverse variational method, based upon the integration tools. Moreover, in this paper, we generalize two aforementioned methods which give new soliton wave solutions. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in engineering and physics fields. By using these methods, exact solutions including the hyperbolic function solution, traveling wave solution, soliton solution, rational function solution, and periodic wave solution of this equation have been obtained. In addition, by using Matlab, some graphical simulations were done to see the behavior of these solutions. 

 © 2019 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: He’s semi-inverse variational principle method, Improved tan (ϕ/2)-expansion method, Nonlinear long-short wave interaction system

 Article History: Received 14 September 2018, Received in revised form 9 March 2019, Accepted 10 June 2019

 Acknowledgement:

No Acknowledgement.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Tekiyeh RM, Manafian J, and Baskonus HM et al. (2019). Applications of He's semi-inverse variational method and ITEM to the nonlinear long-short wave interaction system. International Journal of Advanced and Applied Sciences, 6(8): 53-64

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 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 

 Tables

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