The shock wave solutions of modified ZK Burgers equation in inhomogeneous dusty plasmas

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Liping Zhang ◽  
Jiangqiong Zheng ◽  
Chenxiao Liu ◽  
Jun Ma
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
External Magnetic Field ◽  
Wave Solution ◽  
Burgers Equation ◽  
Dusty Plasmas ◽  
Travelling Wave ◽  
Reductive Perturbation Method ◽  
Wave Transformation ◽  
Shock Wave Solution

Abstract This paper offers a shock wave solution to modified Zakharov–Kuznetsov (MZK) Burgers equation in inhomogeneous dusty plasmas with external magnetic field. For this purpose, the fluid equations are reduced to an MZK Burgers equation containing variable coefficients by reductive perturbation method. With the aid of travelling-wave transformation technique, we obtain the analytical oscillatory shock wave solution and monotonic shock wave solution for MZK Burgers equation. The effects of inhomogeneity, external magnetic field, dust charge variation on characteristics of two types of shock waves are examined in detail.

scholarly journals Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ting Zhang ◽  
Chun Shen
Keyword(s):  
Shock Wave ◽  
Initial Data ◽  
Riemann Problem ◽  
Wave Solution ◽  
Burgers Equation ◽  
Explicit Computation ◽  
Convective Term ◽  
Regularization Technique ◽  
Shock Wave Solution

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.

scholarly journals A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yi-Hu Feng ◽  
Lei Hou
Keyword(s):  
Shock Wave ◽  
Time Delay ◽  
Wave Solution ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Expansion Method ◽  
Initial Boundary ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Shock Wave Solution

Nonlinear singularly perturbed problem for time-delay evolution equation with two parameters is studied. Using the variables of the multiple scales method, homogeneous equilibrium method, and approximation expansion method from the singularly perturbed theories, the structure of the solution to the time-delay problem with two small parameters is discussed. Under suitable conditions, first, the outer solution to the time-delay initial boundary value problem is given. Second, the multiple scales variables are introduced to obtain the shock wave solution and boundary layer corrective terms for the solution. Then, the stretched variable is applied to get the initial layer correction terms. Finally, using the singularly perturbed theory and the fixed point theorem from functional analysis, the uniform validity of asymptotic expansion solution to the problem is proved. In addition, the proposed method possesses the advantages of being very convenient to use.

Shock wave solutions of the variants of the Kadomtsev–Petviashvili equation

2011 ◽  
Vol 89 (9) ◽  
pp. 979-984 ◽  
Author(s):  
Houria Triki ◽  
B.J.M. Sturdevant ◽  
T. Hayat ◽  
O.M. Aldossary ◽  
A. Biswas
Keyword(s):  
Shock Wave ◽  
Wave Solution ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Shock Wave Solution

This study obtained the shock wave or kink solutions of the variants of the Kadomtsev–Petviashvili equation with generalized evolution. There are three types of variants of this equation that were considered. The relation between the parameters and the constraint conditions will naturally fall out as a consequence of the derivation of the shock wave solution.

Effects of dust grain charge fluctuation on an obliquely propagating dust acoustic solitary potential in a magnetized dusty plasma

2000 ◽  
Vol 63 (2) ◽  
pp. 191-200 ◽  
Author(s):  
A. A. MAMUN ◽  
M. H. A. HASSAN
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dusty Plasma ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Charge Fluctuation ◽  
Dust Grains ◽  
Magnetized Dusty Plasma ◽  
Dust Acoustic ◽  
Dust Grain

Effects of dust grain charge fluctuation, obliqueness and external magnetic field on a finite-amplitude dust acoustic solitary potential in a magnetized dusty plasma, consisting of electrons, ions and charge-fluctuating dust grains, are investigated using the reductive perturbation method. It is shown that such a magnetized dusty plasma system may support a dust acoustic solitary potential on a very slow time scale involving the motion of dust grains, whose charge is self- consistently determined by local electron and ion currents. The effects of dust grain charge fluctuation, external magnetic field and obliqueness are found to modify the properties of this dust acoustic solitary potential significantly. The implications of these results for some space and astrophysical dusty plasma systems, especially planetary ring systems and cometary tails, are briefly mentioned.

Dust-acoustic shock waves in a magnetized non-thermal dusty plasma

2014 ◽  
Vol 80 (4) ◽  
pp. 593-606 ◽  
Author(s):  
M. SHAHMANSOURI ◽  
A. A. MAMUN
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Shock Waves ◽  
Dusty Plasma ◽  
Reductive Perturbation Method ◽  
Fluid Viscosity ◽  
Laboratory Plasma ◽  
Basic Properties ◽  
Dust Acoustic ◽  
Dust Fluid

A theoretical investigation is carried out to study the basic properties of dust-acoustic (DA) shock waves propagating in a magnetized non-thermal dusty plasma (containing cold viscous dust fluid, non-thermal ions, and non-thermal electrons). The reductive perturbation method is used to derive the Korteweg–de Vries–Burgers equation. It is found that the basic properties of DA shock waves are significantly modified by the combined effects of dust fluid viscosity, external magnetic field, and obliqueness (angle between external magnetic field and DA wave propagation direction). It is shown that the dust fluid viscosity acts as a source of dissipation, and is responsible for the formation of DA shock structures in the dusty plasma system under consideration. The implications of our results in some space and laboratory plasma situations are briefly discussed.

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