Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5616
Title: Q-Shock soliton evolution
Authors: Pashaev, Oktay
Nalcı, Şengül
Keywords: Polynomials
Control nonlinearities
Exponential functions
Nonlinear equations
Partial differential equations
Arbitrary number
Issue Date: Sep-2012
Publisher: Elsevier Ltd.
Source: Pashaev, O., and Nalcı, Ş. (2012). Q-Shock soliton evolution. Chaos, Solitons and Fractals, 45(9-10), 1246-1254. doi:10.1016/j.chaos.2012.06.013
Abstract: By generating function based on Jackson's q-exponential function and the standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to q-Hermite polynomials with triple recurrence relations similar to [1], our polynomials satisfy multiple term recurrence relations, which are derived by the q-logarithmic function. It allows us to introduce the q-Heat equation with standard time evolution and the q-deformed space derivative. We find solution of this equation in terms of q-Kampe-de Feriet polynomials with arbitrary number of moving zeros, and solved the initial value problem in operator form. By q-analog of the Cole-Hopf transformation we obtain a new q-deformed Burgers type nonlinear equation with cubic nonlinearity. Regular everywhere, single and multiple q-shock soliton solutions and their time evolution are studied. A novel, self-similarity property of the q-shock solitons is found. Their evolution shows regular character free of any singularities. The results are extended to the linear time dependent q-Schrödinger equation and its nonlinear q-Madelung fluid type representation. © 2012 Elsevier Ltd. All rights reserved.
URI: http://doi.org/10.1016/j.chaos.2012.06.013
http://hdl.handle.net/11147/5616
ISSN: 0960-0779
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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