Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Damped Parametric Oscillator and Exactly Solvable Complex Burgers Equations(IOP Publishing Ltd., 2012) Atılgan Büyükaşık, Şirin; Pashaev, Oktay; Pashaev, Oktay; Atılgan Büyükaşık, Şirin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyWe obtain exact solutions of a parametric Madelung fluid model with dissipation which is linearazible in the form of Schrödinger equation with time variable coefficients. The corresponding complex Burgers equation is solved by a generalized Cole-Hopf transformation and the dynamics of the pole singularities is described explicitly. In particular, we give exact solutions for variable parametric Madelung fluid and complex Burgers equations related with the Sturm-Liouville problems for the classical Hermite, Laguerre and Legendre type orthogonal polynomials.Article Citation - WoS: 12Citation - Scopus: 11Q-Analog of Shock Soliton Solution(IOP Publishing Ltd., 2010) Nalcı, Şengül; Pashaev, Oktay; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyBased on Jackson's q-exponential function, we introduce a q-analog of Hermite and Kampe de Feriet polynomials. It allows us to introduce and solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary number of moving zeros, and to find an operator solution for the initial value problem. By the q-analog of Cole-Hopf transformation we find a new q-Burgers-type nonlinear heat equation with cubic nonlinearity, such that in the q → 1 limit it reduces to the standard Burgers equation. We construct exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions. A novel, self-similarity property of the stationary q-shock soliton solution is found. © 2010 IOP Publishing Ltd.