NCTS/TPE-Sinica Seminar on Integrable Systems

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

 
  || Close window ||