Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Subject: search.filters.subject.Shock wavesWoS Q: search.filters.wosQuartile.Q1

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  • Article
    Citation - WoS: 23
    Citation - Scopus: 24
    Exact Solutions of Forced Burgers Equations With Time Variable Coefficients
    (Elsevier Ltd., 2013) Atılgan Büyükaşık, Şirin; Pashaev, Oktay
    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.
  • Article
    Citation - WoS: 43
    Citation - Scopus: 43
    Shock Waves, Chiral Solitons and Semiclassical Limit of One-Dimensional Anyons
    (Elsevier Ltd., 2004) Lee, Jyh Hao; Lin, Chi-Kun; Pashaev, Oktay
    This paper is devoted to the semiclassical limit of the one-dimensional Schrödinger equation with current nonlinearity and Sobolev regularity, before shocks appear in the limit system. In this limit, the modified Euler equations are recovered. The strictly hyperbolicity and genuine nonlinearity are proved for the limit system wherever the Riemann invariants remain distinct. The dispersionless equation and its deformation which is the quantum potential perturbation of JNLS equation are also derived.