Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2622
Title: Q-analog of shock soliton solution
Authors: Nalcı, Şengül
Pashaev, Oktay
Keywords: Special functions
Integrable systems
Solitons
Burgers equation
Issue Date: Nov-2010
Publisher: IOP Publishing Ltd.
Source: Nalcı, Ş., and Pashaev, O. (2010). Q-analog of shock soliton solution. Journal of Physics A: Mathematical and Theoretical, 43(44). doi:10.1088/1751-8113/43/44/445205
Abstract: Based 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.
URI: http://doi.org/10.1088/1751-8113/43/44/445205
http://hdl.handle.net/11147/2622
ISSN: 1751-8113
1751-8121
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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