主講者: | Professor Oktay Pashaev (Izmir Institute of Technology, Turkey) |
講題: | The q-Shock Soliton Solutions and C-Integrable q-Burgers Type Equation |
時間: | 2010-07-09 (Fri.) 15:00 - 16:30 |
地點: | 數學所 722 研討室 (台大院區) |
Abstract: | By using Jackson's q-exponential function we introduce the generating function, the recursion formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the linear q-Heat equation in terms of the 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(joint work with Sengul Nalci). Sponsored by NCTS/TPE and Inst. of Math,Academia Sinica,Taipei |
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