Traveling waves in rational expressions of exponential functions to the conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations

The conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one. The predicted solution is of the form of a rational expression of two finite series at both the numerator and the denominator. The terms of both series are of the powers of some functions having exponential expressions satisfying a particular ODE. The exact solutions are expressed explicitly in terms of powers of some exponential functions in form of rational expressions.

[1]  İsmail Aslan,et al.  Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method , 2008 .

[2]  Wenxiu Ma,et al.  A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation , 2009, 0903.5337.

[3]  Zhang Jie-Fang,et al.  Bäcklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation , 2002 .

[4]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[5]  José António Tenreiro Machado,et al.  What is a fractional derivative? , 2015, J. Comput. Phys..

[6]  Alfred Ramani,et al.  Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable? , 1986 .

[7]  Ma Zheng-Yi,et al.  New exact solutions of a (3+1)-dimensional Jimbo—Miwa system , 2013 .

[8]  EXACT SOLUTION OF FRACTIONAL STO AND JIMBO-MIWA EQUATIONS WITH THE GENERALIZED BERNOULLI EQUATION METHOD , 2014 .

[9]  F. S. Khodadad,et al.  The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative , 2017 .

[10]  C. M. Khalique,et al.  Solutions of Zakharov-Kuznetsov equation with power law nonlinearity in (1+3) dimensions , 2011 .

[12]  M. Hellberg,et al.  The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic waves , 2001 .

[13]  K. Hosseini,et al.  Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods , 2017 .

[14]  Bintao Cao.  Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations , 2009, 0902.3308.

[15]  Woo-Pyo Hong,et al.  New solitonic solutions to a (3+1)-dimensional Jimbo-Miwa equation , 2000 .

[16]  R. Ansari,et al.  Modified Kudryashov method for solving the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities , 2017 .

[17]  Alper Korkmaz,et al.  Exact Solutions to (3+1) Conformable Time Fractional Jimbo–Miwa, Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations , 2017 .

[18]  Wei Zhao,et al.  A new definition of fractional derivative , 2019, International Journal of Non-Linear Mechanics.

[19]  M. Kaplan,et al.  Exact traveling wave solutions of the Wu–Zhang system describing (1 + 1)-dimensional dispersive long wave , 2017 .

[20]  Xi-Qiang Liu,et al.  New solutions of the 3 + 1 dimensional Jimbo-Miwa equation , 2004, Appl. Math. Comput..

[21]  Yuan Liang.  Exact solutions of the (3+1)-dimensional modified KdV-Zakharov- Kuznetsev equation and Fisher equations using the modified simple equation method , 2014 .

[22]  Zhengde Dai,et al.  Exact three-wave solutions for the (3+1)-dimensional Jimbo-Miwa equation , 2011, Comput. Math. Appl..

[23]  D. Baleanu,et al.  New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method , 2017 .

[24]  A. Alsaedi,et al.  New properties of conformable derivative , 2015 .

[25]  Jianzhong Su,et al.  Construction of exact solutions to the Jimbo-Miwa equation through Bäcklund transformation and symbolic computation , 2013, Comput. Math. Appl..

[26]  Manjit Singh.  New exact solutions for (3+1)-dimensional Jimbo–Miwa equation , 2016 .

[27]  Anjan Biswas,et al.  Solitons and other solutions to the quantum Zakharov-Kuznetsov equation , 2012 .

[28]  Adem C. Cevikel,et al.  Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation , 2016 .

[29]  Jian-Ping Fang,et al.  New exact solutions for the (3 + 1)-dimensional Jimbo–Miwa system , 2009 .

[30]  A. Bains,et al.  Zakharov-Kuznetsov equation in a magnetized plasma with two temperature superthermal electrons , 2014 .

[31]  Hadi Rezazadeh,et al.  The first integral method for Wu–Zhang system with conformable time-fractional derivative , 2016 .

[32]  M. Luo,et al.  General conformable fractional derivative and its physical interpretation , 2017, Calcolo.

[33]  Z. Dai,et al.  Abundant new exact solutions for the (3+1)-dimensional Jimbo–Miwa equation , 2010 .

[34]  D. Wen-shan,et al.  New Periodic Wave Solutions, Localized Excitations and Their Interaction Properties for (3+1)-Dimensional Jimbo–Miwa Equation , 2007 .

[35]  Hon-Wah Tam,et al.  SOLITON SOLUTIONS TO THE JIMBO-MIWA EQUATIONS AND THE FORDY-GIBBONS-JIMBO-MIWA EQUATION , 1999 .

[36]  Dumitru Baleanu,et al.  New exact solutions of Burgers’ type equations with conformable derivative , 2017 .

[37]  M. Kaplan,et al.  A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative , 2017 .

[38]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations , 2008, Appl. Math. Comput..

[39]  Vladimir E. Zakharov,et al.  Three-dimensional solitons , 1974 .

[40]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .