Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
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Article Citation - WoS: 23Citation - Scopus: 24Exact Solutions of Forced Burgers Equations With Time Variable Coefficients(Elsevier Ltd., 2013) Atılgan Büyükaşık, Şirin; Pashaev, Oktay; Pashaev, Oktay; Atılgan Büyükaşık, Şirin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn 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.