Conservation laws and multiple simplest equation methods to an extended quantum Zakharov-Kuznetsov equation

Abstract

The extended quantum Zakharov-Kuznetsov (QZK) equation, which arises in the study of astrophysics is investigated. Exact traveling wave solutions are obtained by using distinct types of the simplest equation method namely, the simplest equation method, the extended simplest equation method and the modified simplest equation method. In addition conservation laws via a new conservation theorem are constructed for the underlying equation.

Bright, periodic, compacton and bell-shape soliton solutions of the extended QZK and (3 + 1)-dimensional ZK equations

“…In [46], the optimal system and conservation law were used for further investigation of the extended QZK equation. To obtain the exact travelling wave solutions to the extended QZK equation, El-Ganaini and Akbar [47] contrive the modified simplest equation technique, the extended simplest equation technique, and the simplest equation technique. Baskonus et al [48] extracted hyperbolic and complex function solutions of the extended QZK equation by using the sine-Gordon expansion technique.…”

The new exact solutions of the new coupled Konno-Oono equation by using extended simplest equation method

“…Recently, Bilige et al [15,16], extended and improved this method which is called the extended simplest equation method. After wards, several researchers applied this method to obtain new exact solutions for nonlinear PDEs [15][16][17][18][19][20].…”