Quantum Zakharov-Kuznetsov Research Articles

Dynamical analysis and soliton solutions of a variety of quantum nonlinear Zakharov–Kuznetsov models via three analytical techniques

Some new types of truncated M-fractional exact soliton solutions of the two important quantum plasma physics models, extended quantum Zakharov–Kuznetsov and extended quantum nonlinear Zakharov–Kuznetsov, are successfully achieved by applying the expa function technique, the improved (G′/G)-expansion technique, and the Sardar sub-equation technique. These two models have many useful applications when explaining the waves in the quantum electron-positron-ion magnetoplasmas as well as weakly nonlinear ion-acoustic waves in plasma. The obtained results are in the form of dark, bright, periodic, and other soliton solutions. The results are verified and represented by two-dimensional, three-dimensional, and contour graphs. The results are newer than the existing results in the literature due to the use of fractional derivatives. Hence, the solutions will be fruitful in future studies on these models. The solutions obtained are useful in the areas of applied physics, applied mathematics, dynamical systems, and nonlinear waves in plasmas and in dense space plasma. The applied techniques are simple, fruitful, and reliable for solving other models in mathematical physics.

Diving into plasma physics: dynamical behaviour of nonlinear waves in (3 + 1)-D extended quantum Zakharov–Kuznetsov equation

Diving into plasma physics: dynamical behaviour of nonlinear waves in (3 + 1)-D extended quantum Zakharov–Kuznetsov equation

Qualitative analysis and soliton solutions of nonlinear extended quantum Zakharov-Kuznetsov equation

Qualitative analysis and soliton solutions of nonlinear extended quantum Zakharov-Kuznetsov equation

Wave structures of the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation: analytical insights utilizing two high impact methods

Wave structures of the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation: analytical insights utilizing two high impact methods

Conservation laws, exact solutions and stability analysis for time-fractional extended quantum Zakharov–Kuznetsov equation

Conservation laws, exact solutions and stability analysis for time-fractional extended quantum Zakharov–Kuznetsov equation

Extraction of new soliton solutions of (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation via generalized exponential rational function method and $$\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) $$ expansion method

Extraction of new soliton solutions of (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation via generalized exponential rational function method and $$\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) $$ expansion method

Nonlinear complex dynamical analysis and solitary waves for the (3+1)-D nonlinear extended Quantum Zakharov–Kuznetsov equation

This manuscript is a captivating exploration of the (3+1)-D nonlinear extended Quantum Zakharov–Kuznetsov (NLEQZK) equation, revealing its complex dynamics and solitary wave solutions. We unveil the general method behind this equation and transform it into an ordinary differential equation (ODE), then venture further by using the Galilean transformation to create a system of ODEs. Further, we journey through bifurcations, chaos, and other fascinating dynamical properties, culminating in the visualization and analysis of solitary wave solutions. From the elegant W-shaped solitons to singular solitons with unconventional characteristics and hybrid singular and periodic solitons, each is discussed in vivid detail. This work presents a significant advancement in understanding the unpredictable and intricate behavior of the model, inviting readers to explore the captivating world of non-linear waves and dynamical systems.

Solitary waves solutions and local conserved vectors for extended quantum Zakharov–Kuznetsov equation

Solitary waves solutions and local conserved vectors for extended quantum Zakharov–Kuznetsov equation

Propagation of electrostatic potential with dynamical behaviors and conservation laws of the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation

The [Formula: see text]-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron–positron–ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge–Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented.

Instability of magnetosonic waves in magnetized degenerate half-spin-polarized quantum plasma

Shock and solitary waves in plasmas are the main focus of many current studies of localized disturbances in both laboratory and astrophysical plasmas. Here, the linear and the nonlinear properties evolving in three dimensions quantum magnetized spin-1/2 plasma formed of spin up (↑) and spin down (↓), nonrelativistic degenerate inertialess electrons, and classical ions, are considered. The nonlinear propagation is governed by a quantum Zakharov–Kuznetsov–Burger (QZKB) and QZK equations which are derived by using the multiple scales perturbation technique. The shock and solitary wave structures are dependent on the spin polarization parameter, Bohm potential, Zeeman energy, and dissipative parameter. The first, and the second, orders instability growth rates are also derived by using the small-k perturbation expansion method. The previous parameters affect also the instability growth rates. There is a critical angle below which the first order becomes positive while the second order is negative, and over which the first order disappears and the second order becomes positive. Our present results may be useful in understanding the dynamics in the magnetic pulsars, and also in the magnetic white dwarfs and neutron stars systems where degenerate spin-up and spin-down electrons with dissipative effects can exist.

Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma

In this paper, we consider the (3 + 1)-dimensional fractional-stochastic quantum Zakharov–Kuznetsov equation (FSQZKE) with M-truncated derivative. To find novel trigonometric, hyperbolic, elliptic, and rational fractional solutions, two techniques are used: the Jacobi elliptic function approach and the modified F-expansion method. We also expand on a few earlier findings. The extended quantum Zakharov–Kuznetsov has practical applications in dealing with quantum electronpositron–ion magnetoplasmas, warm ions, and hot isothermal electrons in the presence of uniform magnetic fields, which makes the solutions obtained useful in analyzing a number of intriguing physical phenomena. We plot our data in MATLAB and display various 3D and 2D graphical representations to explain how the stochastic term and fractional derivative influence the exact solutions of the FSEQZKE.

Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics

Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics.

Comparison study of the energy and instability of ion-acoustic solitary waves in magnetized electron–positron–ion quantum plasma

Notably, solitary waves that emerge from the nonlinear properties of plasmas are the main focus of many current studies of localized disturbances in both laboratory and astrophysical plasmas. By applying the reductive perturbation method, we derive the nonlinear homogeneous quantum Zakharov–Kuznetsov (QZK) equation in three-component collisionless quantum plasma consisting of electrons, positrons, and ions in the presence of an external static magnetic field. The solitary wave structures are dependent on the Bohm potential, magnetic field, obliqueness, species Fermi temperatures, and densities. The soliton’s electric field and energy are also derived and investigated, which were found to be reduced as the magnetic field increases. The instability growth rate is also derived by using the small-k perturbation expansion method. The previous parameters affect the instability growth rate as well. A comparison of the energy and instability growth rate behaviour against system parameters is carried out. Large energy and large instability growth rate occur at large values of positron density or lower values of ion density. At zero or small rotation angle, both decrease as the magnetic field increases. Our findings could help us understand the dynamics of magnetic white dwarfs, pulsar magnetospheres, semiconductor plasma, and high-intensity laser-solid matter interaction experiments where e-p-i plasma exists.

Applications of cnoidal and snoidal wave solutions via optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering

The nonlinear evolution equations have a wide range of applications, more precisely in physics, biology, chemistry and engineering fields. This domain serves as a point of interest to a large extent in the world’s mathematical community. Thus, this paper purveys an analytical study of a generalized extended (2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering. The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model. We further reduce the equation using the subalgebras obtained. Besides, more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique. Consequently, we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright, dark, periodic (cnoidal and snoidal), compact-type as well as singular solitons. The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time, are outlined with suitable diagrams. This can be of interest to oceanographers and ocean engineers for future analysis. Furthermore, to visualize the dynamics of the results found, we present the graphic display of each of the solutions. Conclusively, we construct conservation laws of the understudy equation via the application of Noether’s theorem.

Study on the periodic solution of the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

In the current work, we consider the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov (Z-K) equation which is used widely to explain the propagations of the waves arising in plasma physics. The variational theory together with the Hamiltonian method are employed to construct the periodic solution of the equation. As expected, the obtained solution agrees well with the solution by He's variational method, which strongly proves the correctness of the proposed method. Finally, we illustrate the solutions through one example in the form of 3-D and 2-D plots. The obtained results show that the method is simple but effective, which is expected to shed a bright light on the study of the nonlinear partial differential equations arising in physics.

W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

Symmetry analysis for the 2 + 1 generalized quantum Zakharov-Kuznetsov equation

We solve the group classification problem for the 2 + 1 generalized quantum Zakharov-Kuznetsov equation. Particularly we consider the generalized equation , and the time-dependent Zakharov-Kuznetsov equation . Function and , are determine in order the equations to admit additional Lie symmetries. Finally, we apply the Lie invariants to find similarity solutions for the generalized quantum Zakharov-Kuznetsov equation.

He's variational method for the time-space fractal (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

In this paper, we derive a new time-space fractal ()-dimensional extended quantum Zakharov-Kuznetsov (Z-K) equation based on He's fractal derivatives. Then He's variational method, together with the two-scale transform are implemented to seek the solitary wave solution of the fractal equation. The main advantage of the variational method is that it can reduce the order of the differential equation and make the equation more simple. The results show that the method is simple and effective, which is expected to shed a bright light on the study of the fractal nonlinear partial differential equations arising in physics.

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.

A variational principle for the (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

The Zakharov-Kuznetsov equation plays a key role in the plasma physics, and its solution has always been a hot topic, however its variational principle has not been studied. So this paper develops a variational formulation for the (3+1)-dimensional extended quantum Zakharov-Kuznetsov equation by the semi-inverse method, which shows an energy conservation law for the dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma. The whole derivation process is presented in detail. The obtained results in this paper are expected to shed a bright light on the study of theoretical basis for the magnetized plasma.