Bifurcation, similarity reduction, conservation laws and exact solutions of modified-Korteweg-de Vries–Burger equation.

In this paper, non-linear propagation of oscillatory and monotonous DIA shocks in dusty plasma with dust charge fluctuations and small isothermal deviation of electrons is considered. The modified-Korteweg-de Vries–Burger (m-KdVB) equation can be derived by using the reductive perturbation (R-P) method. The variational principle and the conservation laws of the m-KdVB equation are constructed by introducing two special functions. A nonlinear self-adjoint classification of the m-KdVB equation is presented. Based on the Ibragimov's theorem, conservation laws for m-KdVB equation are established. We also study the m-KdVB equations by improved tan ψ (χ) 2 -expansion method. Abundant dark, singular and periodic optical solitons solutions of the model are constructed. Furthermore, additional graphical simulations were performed using mathematica to see the behavior of these solutions. With the help of bifurcation theory of planar dynamical systems, we study bifurcation and phase portrait analysis of traveling wave solution of the m-KdVB equation. [ABSTRACT FROM AUTHOR]