Shock Waves, Variational Principle and Conservation Laws of a Schamel–Zakharov–Kuznetsov–Burgers Equation in a Magnetised Dust Plasma

Abstract

In this article, we investigate a (3+1)-dimensional Schamel–Zakharov–Kuznetsov–Burgers (SZKB) equation, which describes the nonlinear plasma-dust ion acoustic waves (DIAWs) in a magnetised dusty plasma. With the aid of the Kudryashov method and symbolic computation, a set of new exact solutions for the SZKB equation are derived. By introducing two special functions, a variational principle of the SZKB equation is obtained. Conservation laws of the SZKB equation are obtained by two different approaches: Lie point symmetry and the multiplier method. Thus, the conservation laws here can be useful in enhancing the understanding of nonlinear propagation of small amplitude electrostatic structures in the dense, dissipative DIAWs’ magnetoplasmas. The properties of the shock wave solutions structures are analysed numerically with the system parameters. In addition, the electric field of this solution is investigated. Finally, we will study the physical meanings of solutions.

Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation

“…(1.1) is reduced to the classical SZKB equation, which describes the nonlinear plasma-dust ion acoustic waves DIAWs in a magnetized dusty plasma and it is derived using the standard reductive perturbation technique in small amplitude. The coefficients of dispersion b, non-linearity a, mixed derivative c and dissipation d are given in [50,51]. Note that Sahoo and Ray [52] have studied the (3 + 1)dimensional time-fractional mKdV-ZK equation without the Schamel and Burgers terms.…”