Nonlinear self-adjointness, conserved quantities and Lie symmetry of dust size distribution on a shock wave in quantum dusty plasma

Abstract

The current exploration explains new traveling wave profiles by the Lie symmetry approach Here, we derive the (3+1)-dimensional Zakharov–Kuznetsov burgers equation for the shock wave phenomena in plasma with dust-charged particles having quantum effects. The structures of this model are made by Abelian algebra. The considered equation is reduced to an ordinary differential equation by the use of this Abelian algebra. The complete derivation of the classical symmetries of the considered model and reduction corresponding to the first four symmetries has been added. The new auxiliary equation method is implemented for the formation of the new traveling wave structures. The graphical explanation of some obtained results are elaborated in detail. The nonlinear self-adjointness of the considered model is also part of this work. By this concept, we have evaluated the conservation laws of the model. This work is new and does not exist in literature.