Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object Citation - WoS: 2Citation - Scopus: 2Quantum Group Symmetry for Kaleidoscope of Hydrodynamic Images and Quantum States(IOP Publishing, 2019) Pashaev, OktayThe hydrodynamic flow in several bounded domains can be formulated by the image theorems, like the two circle, the wedge and the strip theorems, describing flow by q-periodic functions. Depending on geometry of the domain, parameter q has different geometrical meanings and values. In the special case of the wedge domain, with q as a primitive root of unity, the set of images appears as a regular polygon kaleidoscope. By interpreting the wave function in the Fock-Barman representation as complex potential of a flow, we find modn projection operators in the space of quantum coherent states, related with operator q-numbers. They determine the units of quantum information as kaleidoscope of quantum states with quantum group symmetry of the q-oscillator. Expansion of Glauber coherent states to these units and corresponding entropy are discussed.Article Citation - WoS: 13Citation - Scopus: 14On a 2+1-Dimensional Whitham-Broer System: a Resonant Nls Connection(John Wiley and Sons Inc., 2011) Rogers, Colin; Pashaev, OktayIt is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey-Stewartson I system incorporating a Madelung-Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1-dimensional Kaup-Broer system is exhibited.