Please use this identifier to cite or link to this item:
Title: Q-Shock soliton evolution
Authors: Pashaev, Oktay
Nalcı, Şengül
Keywords: Polynomials
Control nonlinearities
Exponential functions
Nonlinear equations
Partial differential equations
Arbitrary number
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.
ISSN: 0960-0779
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Files in This Item:
File Description SizeFormat 
5616.pdfMakale1.05 MBAdobe PDFThumbnail
Show full item record

CORE Recommender


checked on Jul 12, 2024


checked on Jun 29, 2024

Page view(s)

checked on Jul 15, 2024


checked on Jul 15, 2024

Google ScholarTM



Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.