Extended Zakharov-Kuznetsov Equation Research Articles

Electromagnetic effects on solitons propagation of the (3+1)-dimensional extended Zakharov-Kuznetsov dynamical model with applications

This paper investigates wave solutions and electromagnetic wave phenomena governed by the (3+1)-dimensional extended Zakharov-Kuznetsov equation (EZKE) utilizing the Sardar sub-equation method. With a focus on electromagnetic wave generation and propagation, we rigorously analyze fundamental properties, soliton solutions, and dynamic behaviors of the EZKE. Through this analytical technique, we unravel the complex interplay among various wave types, including solitary waves and electromagnetic structures, elucidating their formation mechanisms and interaction dynamics. Furthermore, we delve into the stability characteristics of the EZKE, enhancing our understanding of its mathematical and physical implications. Our findings not only contribute to theoretical insights into nonlinear wave phenomena in (3+1)-dimensional space but also hold practical significance in plasma physics, nonlinear optics, and electromagnetic wave propagation. This study advances the development of innovative wave manipulation and control techniques, with applications ranging from plasma confinement in fusion devices to the design of advanced photonic devices for telecommunications and sensing purposes.

Nonlinear structure and growth rate of solitary waves for extended Zakharov-Kuznetsov equation in plasma having (r, q) distribution electrons

The Reductive Perturbation Technique (RPT) is used to investigate ion acoustic waves (IAWs) in magnetized plasmas made up of electrons obeying the generalized form of ( r,q ) distribution. The analysis makes use of the Extended Zakharov-Kuznetsov (EZK) equation and the hydrodynamic theory of plasmas. The study investigates the effects of electron flatness ( r ) at low energy and superthermal ( q ) at high energy on the characteristics of IAWs, and the solutions to the EZK equation are plotted for different values of the plasma characteristics, such as the total ion cyclotron frequency, the ion to electron temperature ratio, and the ion-specific heat. The research goes into great detail to estimate the instability threshold and growth rate of these waves by applying a small-k perturbation technique. Overall, this investigation contributes to the better understanding of ion acoustic structures in space plasmas.

Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics

A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for obtaining the exact solution of some reduced transform equations. Finally, by invoking the new conservation theorem developed by Nail H. Ibragimov, the conservation laws of QZK equation have been derived.

Symmetry reduction, conservation laws and acoustic wave solutions for the extended Zakharov–Kuznetsov dynamical model arising in a dust plasma

In this article, we consider the extended Zakharov–Kuznetsov (EZK) equation, which describes the nonlinear plasma dust acoustic waves (DAWs) in a magnetized dusty plasma. Dusty plasmas consist of three components: electrons, highly negatively charged dust grains, and two-temperature ions (low-temperature ions and high-temperature ions). We study the Lie symmetries, reductions, conservation laws and new exact solutions of EZK equations. Conservation laws for EZK equation is derived by applying the new conservation theorem of Ibragimov. Similarity solution for EZK equation will be obtained using Lie symmetry method. We find the Lie symmetries group of EZK equation, using similarity variables, get reduction equation, solving the reduction equations and then get the similarity solution. Solitary wave solutions of the EZK equation are derived from the reduction equation. Thus, some new exact explicit solutions of the EZK equation are obtained.

A (3 + 1)-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation: Bifurcation and traveling wave solutions

This paper studies the (3 + 1) extended Zakharov–Kuznetsov (EZK) dynamical equation that is utilized to describe nonlinear three-dimensional dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma. The bifurcation theory for planar dynamical systems is applied to the EZK equation. For a given restriction on the parameters, some new traveling wave solutions are characterized in terms of Jacobi-elliptic functions. These solutions are clarified in a graphical way. Physically, these wave solutions represent the related electric potential. Based on Maxwell equations, we calculate the corresponding electric magnetic fields, and we clarify them graphically.

Numerical simulation for (3 + 1)D solitary wave of extended Zakharov–Kuznetsov equation in dusty plasma based on lattice Boltzmann method

This paper reports a study on the (3+1)D solitary waves in dusty plasma governed by the extended Zakharov–Kuznetsov (ZK) equation by using the lattice Boltzmann method (LBM). The lattice Boltzmann model is developed and the evolution of (3+1)D solitary wave has been numerical simulated. The validity of the model is verified by numerical experiments. According to the results of numerical experiments the scheme in this work seems to be appropriate for the numerical study of the (3+1)D solitary wave.

Some new solutions of the conformable extended Zakharov-Kuznetsov equation using Atangana-Baleanu conformable derivative

The generalized Riccati equation mapping method, coupled with Atangana?s conformable derivative is implemented to solve non-linear extended Zakharov-Kuznetsov equation which results in producing hyperbolic, trigonometric and the rational solutions. The obtained results are new and are of great importance in engineering and applied sciences.

Solitary wave solutions of (3+1)-dimensional extended Zakharov–Kuznetsov equation by Lie symmetry approach

In this paper, the solitary wave solutions of (3+1)-dimensional extended Zakharov–Kuznetsov (eZK) equation are constructed which appear in the magnetized two-ion-temperature dusty plasma and quantum physics. Lie group of transformation method is proposed to investigate the solution of (3+1)-dimensional eZK equation via Lie symmetry method. The optimal system of one dimensional Lie subalgebra is constructed by using Lie point symmetries. The three dimensional eZK equation reduced into number of ordinary differential equations (ODEs) by applying similarity reductions. Consequently, solutions so extracted are more general than erstwhile known results. We have obtained twenty one solutions in the explicit form, some of them are likewise general and some are new for the best study of us. Eventually, single soliton, quasi-periodic soliton, multisoliton, lump-type soliton, traveling wave and solitary wave-interaction behavior are illustrated graphically through numerical simulation for physical affirmation of the results. Please check whether the affiliations are correct.

Soliton Solutions of Space-Time Fractional-Order Modified Extended Zakharov-Kuznetsov Equation in Plasma Physics

The aim of this article is to calculate the soliton solutions of space-time fractional-order modified extended Zakharov-Kuznetsov equation which is modeled to investigate the waves in magnetized plasma physics. Fractional derivatives in the form of modified Riemann-Liouville derivatives are used. Complex fractional transformation is applied to convert the original nonlinear partial differential equation into another nonlinear ordinary differential equation. Then, soliton solutions are obtained by using (1/G')-expansion method. Bright and dark soliton solutions are also obtain with ansatz method. These solutions may be of significant importance in plasma physics where this equation is modeled for some special physical phenomenon.

Response to “Comment on ‘Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma’” [Phys. Plasmas 25, 104701 (2018)

On our previous soliton solutions [H. L. Zhen et al., Phys. Plasmas 21, 073709 (2014)] of an extended Zakharov-Kuznetsov equation, El-Tantawy and Wazwaz [Phys. Plasmas 25, 104701 (2018)] have commented that there exists another soliton solution without any constraint for the parameters. In this Reply, we first state the correctness of our previous solutions, and then, we point out the difference between the two solutions: one is from our previous paper [H. L. Zhen et al., Phys. Plasmas 21, 073709 (2014)] and the other is from the comment by El-Tantawy and Wazwaz [Phys. Plasmas 25, 104701 (2018)]. Meanwhile, we also investigate the connections between our work and some recent literature studies.

On the analytical solutions of conformable time-fractional extended Zakharov–Kuznetsov equation through ( $$G'/G^{2}$$ G ′ / G 2 )-expansion method and the modified Kudryashov method

The aim of this article is to obtain and study the solutions of conformable time fractional (1+2)-dimensional extended Zakharov–Kuznetsov equation (2D-FZKE) which is modeled to investigate the waves in magnetized plasma. Wave transformation in fractional form is applied to convert the original fractional order nonlinear partial differential equation into another nonlinear ordinary differential equation. The strategy here consists of using ( $$G'/G^{2}$$ )-expansion method and the modified Kudryashov method to obtain a variety of exact solutions. Both schemes work well and reveal distinct exact solutions. These solutions are of significant importance in plasma physics where the 2D-FZKE is modeled for some special physical phenomenon.

The stability of the dust acoustic waves under transverse perturbations in a magnetized and collisionless dusty plasma

Numerical and theoretical investigations are carried out for the stability of the dust acoustic waves (DAWs) under the transverse perturbation in a two-ion temperature magnetized and collisionless dusty plasma. The Zakharov-Kuznetsov (ZK) equation, modified ZK equation, and Extended ZK (EZK) equation of the DAWs are given by using the reductive perturbation technique. The cut-off frequency is obtained by applying higher-order transverse perturbations to the soliton solution of the EZK equation. The propagation velocity of solitary waves, the real cut-off frequency, as well as the growth rate of the higher-order perturbation to the solitary wave are obtained.

Nonlinear dynamics associated with rotating magnetized electron–positron–ion plasmas

By using the hydrodynamic equations of electrons and positrons and Poisson equation with stationary ions, a three-dimensional extended Zakharov–Kuznetsov (EZK) equation is derived for small but finite amplitude nonlinear Langmuir structures (solitary and shock pulses) The EZK equation is solved analytically and the features of the nonlinear excitations are investigated numerically. Furthermore, the propagation condition for the nonlinear structures is examined.

Nonlinear Langmuir structures: Soliton and shock in a rotating weakly relativistic electron-positron magnetoplasma with stationary positive ions

Theoretical and numerical studies are performed for nonlinear Langmuir structures (soliton and shock) in a rotating weakly relativistic electron-positron magnetoplasma with background stationary positive ions. For this purpose, the reductive perturbation technique is employed to the weakly relativistic hydrodynamical electrons/positrons fluid equations and Poisson equation, obtaining extended Zakharov–Kuznetsov equation. The latter has been solved analytically. The features of the nonlinear excitations and their propagation conditions are investigated numerically. Our finding could elucidate the nonlinear electrostatic structures that propagate in astrophysical plasma situations where rotating, magnetized plasma can exist; such as polar cups region of pulsars, around active galactic nuclei, neutron stars, and white dwarfs.