2020Thermal ScienceOpen access

The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

Xiaojun Yin, Quansheng Liu, Liangui Yang, N Narenmandula

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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 expan?sion 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.

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What this paper is about

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 expan?sion 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.

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Available 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 expan?sion 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.

Key concepts: Riccati equation, Soliton, Kadomtsev–Petviashvili equation, Physics, Algebraic Riccati equation, Quantum, Mathematical physics, Applied mathematics

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