Abstract
Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.
Highlights
We investigate Lie group classification of two different cases of the generalized variable coefficient Korteweg-de Vrie (KdV) equation with dual power-law nonlinearities and linear damping dispersion ((1+1)D-gvcKdVDampe) in quantum field theory which is expressed as: ut + Q(t)un u x + S(t)u2m u x + H (t)u + G (t)u xxx = 0 (3)
Invoking Lemma (1), we present the minimal differential order of Langrangian corresponding to variable coefficient nonlinear partial differential Equation (118) as:
We investigated the generalized variable coefficient Korteweg-de Vries equation with linear damping term in quantum field theory
Summary
It is a known fact that many physical phenomena are represented by NLEVEQ as well as its higher-order form with variable coefficients because the vast majority of genuine nonlinear physical conditions involve variable coefficients. Scientists in their numbers have deemed it fit to contemplate nonlinear science as the most significant frontier for the fundamental comprehension of nature. The modified and generalized Zakharov–Kuznetsov model, which recounts the ion-acoustic drift solitary waves existing in a magnetoplasma with electron-positron-ion which are found in the primordial universe was investigated in [3,4].
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