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Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a time-dependent function. Using a Waynes transformation and centre manifold theory, we derive l-mode and 2-mode centre manifold models of the generalised Burgers equations for bounded smooth time dependent coefficients. These modellings give some interesting extensions to existing results such as the similarity solutions using the similarity method.
The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two arbitrary function
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogen
this paper we show some new exact solutions for the generalized modified Degasperis$-$Procesi equation (mDP equation)
In this paper we show some new exact solutions for the generalized modified Degasperis$-$Procesi equation (mDP equation)
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite in