Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5172
Title: Exact solutions of forced Burgers equations with time variable coefficients
Authors: Atılgan Büyükaşık, Şirin
Pashaev, Oktay
Keywords: C-integrable
Exact solutions
Forced Burgers equation
Pole dynamics
Variable parameters
Shock waves
Partial differential equations
Issue Date: Jul-2013
Publisher: Elsevier Ltd.
Source: Atılgan Büyükaşık, Ş., and Pashaev, O. (2013). Exact solutions of forced Burgers equations with time variable coefficients. Communications in Nonlinear Science and Numerical Simulation, 18(7), 1635-1651. doi:10.1016/j.cnsns.2012.11.027
Abstract: In this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ̇(t)/μ(t))U+UUx=(1/2μ(t))Uxx-ω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described.
URI: https:doi.org/10.1016/j.cnsns.2012.11.027
http://hdl.handle.net/11147/5172
ISSN: 1007-5704
1007-5704
1878-7274
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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