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Title: Dynamical properties of generalized traveling waves of exactly solvable forced Burgers equations with variable coefficients
Authors: Atılgan Büyükaşık, Şirin
Bozacı, Aylin
Keywords: Burgers equation
Variable coefficients
Exact solutions
Wei-Norman Lie algebraic approach
Issue Date: 2021
Publisher: Elsevier
Abstract: The initial value problem for a generalized forced Burgers equation with variable coefficients U-t + ((mu)over dot(t)/mu(t))U + UUX = (1/2 mu(t))U-xx - a(t)U-x + b(t)(xU)(x) - omega(2)(t)x + f(t), x is an element of R , t > 0, is solved using Cole-Hopf linearization and Wei-Norman Lie algebraic approach for finding the evolution operator of the associated linear diffusion type equation. As a result, solution of the initial value problem is obtained in terms of a corresponding linear second-order inhomogeneous ordinary differential equation and a standard Burgers model. Then, using the translation and Galilean invariance of standard Burgers equation, families of generalized nonlinear waves propagating according to a Newtonian type equation of motion are constructed. The influence of the damping, dilatation and forcing terms on the dynamics of shocks, multi-shocks, triangular and N-shaped generalized traveling waves and rational type solutions with moving singularities is investigated. Finally, exactly solvable models with concrete time-variable coefficients are introduced and dynamical properties of certain particular solutions are discussed. (C) 2020 Elsevier B.V. All rights reserved.
ISSN: 1007-5704
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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