Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
Browse
3 results
Search Results
Article Citation - WoS: 91Citation - Scopus: 91Resonance Solitons as Black Holes in Madelung Fluid(World Scientific Publishing Co. Pte Ltd, 2002) Pashaev, Oktay; Lee, Jyh HaoEnvelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For s < 1, the model is equivalent to the usual NLS with rescaled coupling constant, while for s > 1, to the reaction-diffusion system. The last one is related to the anti-de Sitter (AdS) space valued Heisenberg model, realizing a particular gauge fixing condition of the (1 + 1)-dimensional Jackiw-Teitelboim gravity. For this gravity model, by the Madelung fluid representation we derive the acoustic form of the space-time metric. The space-time points, where dispersion changes the sign, correspond to the event horizon, while the soliton solution to the AdS black hole. Moving with the above bounded velocity, it describes evolution on the one sheet hyperboloid with nontrivial winding number, and creates under collision, the resonance states which we study by the Hirota bilinear method.Conference Object Citation - WoS: 6Citation - Scopus: 6Soliton Resonances, Black Holes and Madelung Fluid(Taylor and Francis Ltd., 2001) Pashaev, Oktay; Lee, Jyh HaoThe reaction-diffusion system realizing a particular gauge fixing condition of the Jackiw-Teitelboim gravity is represented as a coupled pair of Burgers equations with positive and negative viscosity. For acoustic metric in the Madelung fluid representation the space-time points where dispersion change the sign correspond to the event horizon, while shock soliton solutions to the black holes, creating under collision the resonance states.Conference Object Citation - WoS: 2Citation - Scopus: 2Self-Dual Chern-Simons Solitons and Quantum Potential(Taylor and Francis Ltd., 2001) Pashaev, Oktay; Lee, Jyh HaoAn influence of the quantum potential on the Chern-Simons solitons leads to quantization of the statistical parameter κ = me 2/g, and the quantum potential strength s = 1 - m 2. A new type of exponentially localized Chern-Simons solitons for the Bloch electrons near the hyperbolic energy band boundary are found.