Speaker : Oktay Pashaev (Izmir Institute of Technology)
Title : Dynamical Symmetry, q-Semiclassical Expansion and Shock Soliton Fission in q- Viscous Burgers’ Equation
Time : 2018-08-29 (Wed) 15:00 - 16:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: Motivated by q-deformed quantum oscillator, we propose a new type of heat equation with non-symmetric q-extension of the diffusion term. Rewritten for the relative gradient field, this q-diffusive heat equation appears as the q-viscous Burgers’ equation from the Burgers’ hierarchy. Exact solutions of this equation in the form of generalized Kampe de Feriet polynomials, corresponding dynamical symmetry and description in terms of Bell polynomials are derived. The generating function for the polynomials is obtained by application of dynamical symmetry operators and the Zassenhaus formula. Shock soliton solutions and their interactions are found and analyzed for different values of q. For q < 1 the soliton speed becomes bounded from the above by the maximal value. This implies that in addition to usual Burgers solitons fusion, our q-viscous shock solitons show a new phenomenon, when soliton with higher amplitude but smaller velocity is fissing to two solitons. The q-semiclassical expansion of equations and corresponding solutions in terms of Bernoulli polynomials are developed.