q-Analogue of Shock Soliton Solution
By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes...
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| creator | Sengul Nalci Pashaev, Oktay K |
| description | By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found. |
| doi_str_mv | 10.48550/arxiv.1005.2543 |
| format | Article |
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This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1005.2543</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Boundary value problems ; Burgers equation ; Differential equations ; Exponential functions ; Hermite polynomials ; Markov analysis ; Nonlinearity ; Operators (mathematics) ; Physics - Exactly Solvable and Integrable Systems ; Quadratic equations ; Recursive functions ; Thermodynamics</subject><ispartof>arXiv.org, 2010-05</ispartof><rights>2010. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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| subjects | Boundary value problems Burgers equation Differential equations Exponential functions Hermite polynomials Markov analysis Nonlinearity Operators (mathematics) Physics - Exactly Solvable and Integrable Systems Quadratic equations Recursive functions Thermodynamics |
| title | q-Analogue of Shock Soliton Solution |
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