Seminar on Integrable Systems
主講者: Oktay Pashaev (Izmir Inst. of Technology, Turkey)
講題: Nonlinearity and quantum potential
時間: 2008-01-24 (Thu.)  16:00-17:00
Abstract: The Quantum Potential (QP) first introduced by L. de Broglie to solve wave- particle dualism problem in quantum mechanics, and explored by D. Bohm and E. Madelung for interpretations of quantum theory, recently attracted attention from different fields of physics. It appears in attempts to quantize gravity theory, Nelson stochastic quantization, Schrodinger zitterbewegung, Fisher information and etc. In the present talk I will discuss applications of this potential to nonlinear integrable systems. I will discuss NLS, DNLS equations with QP, their dispersionless limit and the resonance character of soliton dynamics. Description of magneto-acoustic waves in plasma physics and anyons in Quantum Hall type systems . Some geometrical applications to pseudo-Riemmanian surfaces and black holes solutions in low dimensional gravity. Finally its influence on the auxiliary linear problem and resonances of 2+1 dimensional integrable systems like KP , MKP and Davey-Stewartson
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