Tbilisi Mathematical Journal

Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

Yücel Çenesiz, Orkun Tasbozan, and Ali Kurt

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Abstract

Modeling the motion and propagation characteristics of waves have importance in coastal, ocean and maritime engineering. Especially, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures in most geographical areas. So Maccari system has great application in mentioned areas. The modified KdV is ion acoustic perturbations evolution model in a plasma with two negative ion components which have different temperatures. As for the KdV equation, the modified ZK (mZK) equation arises naturally as weakly two-dimensional variations of the mKdV equation. In this paper authors used functional variable method(FVM) for the first time to obtain exact travelling wave and soliton solutions of conformable fractional modified KdV-Zakharov-Kuznetsov(mKdv-ZK) equation and Maccari system. As a consequence, new solutions are obtained and it is seen that FVM is an valuable and efficient tool for solving nonlinear equations and systems where the derivatives defined by means of conformable fractional derivative.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 1 (2017), 117-125.

Dates
Received: 20 May 2016
Accepted: 7 July 2016
First available in Project Euclid: 26 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1527300021

Digital Object Identifier
doi:10.1515/tmj-2017-0010

Mathematical Reviews number (MathSciNet)
MR3610024

Zentralblatt MATH identifier
1372.35330

Subjects
Primary: 35R11: Fractional partial differential equations
Secondary: 34A08: Fractional differential equations 35A20: Analytic methods, singularities 26A33: Fractional derivatives and integrals

Keywords
Functional Variable Method KdV-Zakharov-Kuznetsov Equation Maccari System Conformable Fractional Derivative

Citation

Çenesiz, Yücel; Tasbozan, Orkun; Kurt, Ali. Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system. Tbilisi Math. J. 10 (2017), no. 1, 117--125. doi:10.1515/tmj-2017-0010. https://projecteuclid.org/euclid.tbilisi/1527300021


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