Mathematics / Matematik

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Institution Author: search.filters.institutionAuthor.Nalcı, ŞengülSubject: search.filters.subject.Integrable systems

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  • Article
    Citation - WoS: 12
    Citation - Scopus: 11
    Q-Analog of Shock Soliton Solution
    (IOP Publishing Ltd., 2010) Nalcı, Şengül; Pashaev, Oktay
    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.