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Browsing WOS by Author "Buyukasik, Sirin A."

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    Journal Article
    Citation - WoS: 23
    Exact solutions of forced burgers equations with time variable coefficients
    (Elsevier, 2013) Buyukasik, Sirin A.; Pashaev, Oktay K.
    In this paper, we consider a forced Burgers equation with time variable coefficients of the form U-t + (mu(t)/mu(t))U + UUx = (1/2 mu(t))U-xx - omega(2)(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. (c) 2012 Elsevier B.V. All rights reserved.
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    Journal Article
    Citation - WoS: 3
    Exactly solvable madelung fluid and complex burgers equations: a quantum sturm-liouville connection
    (Springer, 2012) Buyukasik, Sirin A.; Pashaev, Oktay K.
    Quantum Sturm-Liouville problems introduced in our paper (BuyukaAYA +/- k et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, in the present paper we study a set of variable parametric nonlinear Madelung fluid models and corresponding complex Burgers equations, related to the classical orthogonal polynomials of Hermite, Laguerre and Jacobi types. We show that the nonlinear systems admit direct linearazation in the form of Schrodinger equation for a parametric harmonic oscillator, allowing us to solve exactly the initial value problems for these equations by the linear quantum Sturm-Liouville problem. For each type of equations, dynamics of the probability density and corresponding zeros, as well as the complex velocity field and related pole singularities are studied in details.