New exact periodic elliptic wave solutions for extended quantum Zakharov–Kuznetsov equation

In this paper, the exact solutions of extended quantum Zakharov–Kuznetsov (QZK) equation which arises in hydrodynamic that describe the nonlinear propagation of the quantum ion-acoustic waves have been procured. The trial equation method with the discrimination system of polynomials is employed to find the analytical solutions. The local time fractional derivative is used in place of ordinary derivatives to get fractional model. Some plentiful new exact traveling wave solutions of nonlinear extended QZK equation are constructed. The solutions consist of singular, Jacobi elliptic and dark soliton solutions. Furthermore, the constraint conditions for the existence of these solutions are also presented.

[1]  Mingliang Wang,et al.  Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation , 2005 .

[2]  M. Belić,et al.  Nematicons in liquid crystals by extended trial equation method , 2017 .

[3]  Yücel Çenesiz,et al.  On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System , 2017 .

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

[5]  R. Ansari,et al.  Bright and singular soliton solutions of the conformable time-fractional Klein–Gordon equations with different nonlinearities , 2018 .

[6]  I. Podlubny.  Fractional differential equations , 1998 .

[7]  R. Ansari,et al.  Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the exp(-.PHI.(.EPSILON.))-expansion method , 2017 .

[8]  Constantin Fetecau,et al.  Effects of the fractional order and magnetic field on the blood flow in cylindrical domains , 2016 .

[9]  M. Tribeche,et al.  Weakly Nonlinear Quantum Dust Ion-Acoustic Waves , 2013 .

[10]  M. Belić,et al.  Parallel propagation of dispersive optical solitons by extended trial equation method , 2017 .

[11]  R. Ansari,et al.  Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the $$\exp \left( { - \phi \left( \varepsilon \right)} \right)$$exp-ϕε-expansion method , 2017 .

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

[13]  Bo Yu,et al.  Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids , 2017, Commun. Nonlinear Sci. Numer. Simul..

[14]  M. Younis,et al.  Optical solitons with time fractional nonlinear Schrödinger equation and competing weakly nonlocal nonlinearity , 2017 .

[15]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[16]  M. Eslami,et al.  Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion , 2016 .

[17]  A. H. Khater,et al.  Applications of elliptic functions to ion-acoustic plasma waves , 2008 .

[18]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[19]  Yong Wang,et al.  Fractional Order Systems Time-Optimal Control and Its Application , 2017, J. Optim. Theory Appl..

[20]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[21]  M. Mirzazadeh,et al.  Exact solitons of the coupled sine-Gordon equation in nonlinear system , 2017 .

[22]  Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform , 2016 .

[23]  M. Younis,et al.  Soliton solutions for quintic complex Ginzburg-Landau model , 2017 .

[24]  Ali Saleh Alshomrani,et al.  Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction , 2017 .

[25]  G. Bluman,et al.  Symmetries and differential equations , 1989 .

[26]  Hai-Ping Zhu,et al.  Combined Akhmediev breather and Kuznetsov–Ma solitons in a two-dimensional graded-index waveguide , 2014 .

[27]  R. Ansari,et al.  New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method , 2017 .

[28]  Qin Zhou,et al.  Explicit solitons in the parabolic law nonlinear negative-index materials , 2017 .

[29]  A. Biswas,et al.  Optical solitons in birefringent fibers with Kerr nonlinearity by exp-function method , 2017 .

[30]  Anjan Biswas,et al.  Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics , 2016 .

[31]  M. Eslami,et al.  Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities , 2016 .

[32]  M. Younis,et al.  Optical dark and dark-singular solitons with anti-cubic nonlinearity , 2017 .

[33]  N. Raza,et al.  On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients , 2018 .

[34]  Anjan Biswas,et al.  1-soliton solution of the Zakharov–Kuznetsov equation with dual-power law nonlinearity , 2009 .

[35]  M. Belić,et al.  Optical solitons with DWDM technology and four-wave mixing , 2017 .

[36]  Abdul-Majid Wazwaz,et al.  The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations , 2005 .

[37]  M. Mirzazadeh,et al.  Optical solitons of some fractional differential equations in nonlinear optics , 2017 .

[38]  A. Biswas,et al.  Optical solitons with anti-cubic nonlinearity by extended trial equation method , 2017 .

[39]  M. Mirzazadeh,et al.  Analytical study of solitons in the fiber waveguide with power law nonlinearity , 2017 .

[40]  H. Srivastava,et al.  Local Fractional Integral Transforms and Their Applications , 2015 .

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

[42]  F. Haas,et al.  Modified Zakharov equations for plasmas with a quantum correction , 2004, physics/0410251.