scholarly journals Mathematical methods and solitary wave solutions of three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma and its applications

2017 ◽  
Vol 7 ◽  
pp. 4269-4277 ◽  
Author(s):  
Abdullah ◽  
Aly R. Seadawy ◽  
Wang Jun
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Mathematical Methods ◽  
Wave Solutions

Diverse bistable dark novel explicit wave solutions of cubic–quintic nonlinear Helmholtz model

2021 ◽  
pp. 2150441
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
General Model ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Computational Schemes ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma

2018 ◽  
Vol 33 (25) ◽  
pp. 1850145 ◽  
Author(s):  
Abdullah ◽  
Aly R. Seadawy ◽  
Jun Wang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Electrostatic Field ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

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