New solitary wave solutions for the conformable Klein-Gordon equation with quantic nonlinearity

Mustafa Inc; Hadi Rezazadeh; Javad Vahidi; Mostafa Eslami; Mehmet Ali Akinlar; Muhammad Nasir Ali; Yu-Ming Chu; Mustafa Inc; Hadi Rezazadeh; Javad Vahidi; Mostafa Eslami; Mehmet Ali Akinlar; Muhammad Nasir Ali; Yu-Ming Chu

doi:10.3934/math.2020447

AIMS Mathematics

2020, Volume 5, Issue 6: 6972-6984. doi: 10.3934/math.2020447

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Research article

New solitary wave solutions for the conformable Klein-Gordon equation with quantic nonlinearity

1.
Department of Mathematics, Firat University, Elazig, Turkey
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
3.
Faculty of Engineering Technology, Amol University of Special Modern Technology, Amol, Iran
4.
Department of Applied Mathematics, Iran University of Science and Technology, Tehran, Iran
5.
Department of Mathematics, University of Mazandaran, Babolsar, Iran
6.
Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
7.
National University of Computer and Emerging Sciences, Fast, Lahore, Pakistan
8.
Department of Mathematics, Huzhou University, Huzhou 313000, China
9.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China

Received: 16 June 2020 Accepted: 03 September 2020 Published: 09 September 2020
MSC : 35A09, 35E05

We present new exact solutions in the form of solitary waves for the conformable Klein-Gordon equation with quintic nonlinearity. We use functional variable method which converts a conformable PDE to a second-order ordinary differential equation through a traveling wave transformation. We obtain periodic wave and solitary wave solutions including particularly kink-profile and bell-profile type solutions. The present method is a direct and concise technique which has the potential to be applicable to many other conformable PDEs arising in physics and engineering.
- functional variable technique,
- conformable derivative,
- conformable Klein-Gordon with quantic nonlinearity,
- exact wave solutions
Citation: Mustafa Inc, Hadi Rezazadeh, Javad Vahidi, Mostafa Eslami, Mehmet Ali Akinlar, Muhammad Nasir Ali, Yu-Ming Chu. New solitary wave solutions for the conformable Klein-Gordon equation with quantic nonlinearity[J]. AIMS Mathematics, 2020, 5(6): 6972-6984. doi: 10.3934/math.2020447

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Abstract

We present new exact solutions in the form of solitary waves for the conformable Klein-Gordon equation with quintic nonlinearity. We use functional variable method which converts a conformable PDE to a second-order ordinary differential equation through a traveling wave transformation. We obtain periodic wave and solitary wave solutions including particularly kink-profile and bell-profile type solutions. The present method is a direct and concise technique which has the potential to be applicable to many other conformable PDEs arising in physics and engineering.

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