THERMAL SCIENCE
International Scientific Journal
THE NEW EXACT SOLITARY SOLUTIONS FOR THE (3+1)-DIMENSIONAL ZAKHAROV-KUZNETSOV EQUATION USING THE RICCATI EQUATION
ABSTRACT
In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expansion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.
KEYWORDS
PAPER SUBMITTED: 2020-05-01
PAPER REVISED: 2020-08-01
PAPER ACCEPTED: 2020-08-25
PUBLISHED ONLINE: 2020-11-27
THERMAL SCIENCE YEAR
2020, VOLUME
24, ISSUE
Issue 6, PAGES [3995 - 4000]
- Seadawy, A. R., Stability Analysis Solutions for Nonlinear Three-Dimensional Modified Korteweg-De Vries-Zakharov-Kuznetsov Equation in a Magnetized Electron-Positron Plasma, Physica A, 455 (2016), C, pp. 44-51
- Yu, W.-T., et al., Phase Shift, Amplification, Oscillation and Attenuation of Solitons in Nonlinear Optics, Journal of Advanced Research, 15 (2019), Jan., pp. 69-76
- Yang H.-W., et al., A new ZK-BO Equation for Three-Dimensional Algebraic Rossby Solitary Waves and its Solution as Well as Fission Property, Nonlinear Dynamics, 91 (2018), Dec., pp. 2019-2032
- Yin, X.-J., et al., (2+1)-Dimensional ZK-Burgers Equation with the Generalized Beta Effect and its Exact Solitary Solution, Computers & Mathematics with Applications, 77 (2019), 1, pp. 302-310
- Liu, Q.-S., et al., A New Model Equation for Nonlinear Rossby Waves and Some of its Solutions, Physics Letters A, 383 (2019), 6, pp. 514-525
- Wazwaz, A. M., The Extended Tanh Method for the Zakharov-Kuznetsov (ZK) Equation, the Modified ZK Equation, and its Generalized Forms, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 6, pp. 1039-1047
- Osman, M. S., et al., The Unified Method for Conformable Time Fractional Schrodinger Equation with Perturbation Terms, Chinese Journal of Physics, 56 (2018), 5, pp. 2500-2506
- Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84 (2016), Apr., pp. 3-7
- Liu, Q.-S., et al., Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas, Complexity, 2020 (2020), ID 9075823
- Kuo, C., The New Exact Solitary and Multi-Soliton Solutions for the (2+1)-Dimensional Zakharov-Kuznetsov Equation, Computers & Mathematics with Applications, 75 (2018), 8, pp. 2851-2857
- Yang, X. J., A New Integral Transform Operator for Solving the Heat-diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
- Biswas, A., Solitary Wave Solution of the Zakharov-Kuznetsov Equation in Plasmas with Power Law Nonlinearity, Nonlinear Analysis, 11 (2010), 4, pp. 3272-3274
- Zayed, E. M., et al., On Solving the (3+1)-Dimensional NLEQZK Equation and the (3+1)-Dimensional NLmZK Equation Using the Extended Simplest Equation Method, Computers & Mathematics with Applications, 78 (2019), 10, pp. 3390-3407