Extended 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.

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.

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.

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.

Analytical solutions for the (3＋1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov equation in plasma physics

In the current study, we investigate the (3＋1)-dimensional extended quantum Zakharov–Kuznetsov equation through two different methods namely the sine–Gordon expansion method and the (1∕G′)-expansion method. The given model represent the nonlinear propagation of the quantum ion-acoustic wave. Traveling wave transformation has been used, in order to convert the governing equation into a non-linear ordinary differential equation. As a result, we successfully construct various exact wave solutions, such as shock, topological, non-topological solutions, periodic wave solutions, and singular solutions. In addition, 2D, 3D and contour surfaces are plotted according to the appropriate parameters values.

Some Applications of the (G′/G,1/G)-Expansion Method for Finding Exact Traveling Wave Solutions of Nonlinear Fractional Evolution Equations

In this paper, the ( G ′ / G , 1 / G ) -expansion method is applied to acquire some new, exact solutions of certain interesting, nonlinear, fractional-order partial differential equations arising in mathematical physics. The considered equations comprise the time-fractional, (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation, and the space-time-fractional generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system in the sense of the conformable fractional derivative. Applying traveling wave transformations to the equations, we obtain the corresponding ordinary differential equations in which each of them provides a system of nonlinear algebraic equations when the method is used. As a result, many analytical exact solutions obtained of these equations are expressed in terms of hyperbolic function solutions, trigonometric function solutions, and rational function solutions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions, solitary wave solutions of kink type, and so on. The method is very efficient, powerful, and reliable for solving the proposed equations and other nonlinear fractional partial differential equations with the aid of a symbolic software package.

On solving the (3+1)-dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method

The extended simplest equation method is employed in this article to construct many solitons and other solutions for two nonlinear partial differential equations (PDEs), namely the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation which play an important role in mathematical physics. The first equation is performed in quantum electron–positron–ion magnetoplasmas, while the second equation governs the behavior of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Comparison of our new results obtained in this article for the two considered models with the other well-known results is also provided.

New exact periodic elliptic wave solutions for extended quantum Zakharov–Kuznetsov equation

In this paper, the exact solutions of extended quantum Zakharov–Kuznetsov (QZK) equation which arises in hydrodynamic that describe the nonlinear propagation of the quantum ion-acoustic waves have been procured. The trial equation method with the discrimination system of polynomials is employed to find the analytical solutions. The local time fractional derivative is used in place of ordinary derivatives to get fractional model. Some plentiful new exact traveling wave solutions of nonlinear extended QZK equation are constructed. The solutions consist of singular, Jacobi elliptic and dark soliton solutions. Furthermore, the constraint conditions for the existence of these solutions are also presented.

Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation

In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.