Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma

Abstract

Bifurcations of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation are examined in a dense quantum (DQ) plasma comprising of positive ions, electrons and positrons utilizing reductive perturbation technique (RPT) and the concept of dynamical system for the first time. Using RPT and travelling wave transformation, the model equations are converted to a dynamical system. Existence of kink, anti-kink and periodic wave solutions is shown through phase plot and time series plot based on suitable parametric conditions on coefficient of viscosity ($$\eta $$), density ratio of electrons and ions ($$\mu $$) and wave velocity (V). Depending on different parameters, variation of anti-kink, kink and periodic waves is depicted through numerical simulation. The periodic wave of the Burgers equation due to the periodic orbit is offered for the first time in plasmas through Jacobi elliptic function. It is seen that physical parameters $$\eta ,~\mu $$ and V significantly influence amplitude and smoothness of the kink, anti-kink and periodic wave profiles. The output of this contribution may be utilized to interpret the bifurcation behaviour of periodic, kink and anti-kink waves in DQ plasmas with viscosity effect.