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Browsing Mathematics / Matematik by Author "Lee, Jyh Hao"
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Black holes and solitons of the quantized dispersionless NLS and DNLS equations
Pashaev, Oktay; Lee, Jyh Hao (Cambridge University Press, 200207)The classical dynamics of nonrelativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of ... 
Chiral resonant solitons in ChernSimons theory and BroerKaup type new hydrodynamic systems
Lee, Jyh Hao; Pashaev, Oktay (Elsevier, 201208)New BroerKaup type systems of hydrodynamic equations are derived from the derivative reactiondiffusion systems arising in SL(2, R) KaupNewell hierarchy, represented in the nonMadelung hydrodynamic form. A relation with ... 
Dissipative hierarchies and resonance solitons for KPII and MKPII
Francisco, Meltem L. Y.; Lee, Jyh Hao; Pashaev, Oktay (Elsevier, 200703)We show that dissipative solitons (dissipatons) of the second and the third members of SL(2,R) AKNS hierarchy give rise to the real solitons of KPII, while for SL(2,R) KaupNewell hierarchy they give solitons of MKPII. ... 
Relativistic DNLS and KaupNewell hierarchy
Pashaev, Oktay; Lee, Jyh Hao (Institute of Mathematics, 201707)By the recursion operator of the KaupNewell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit c → ∞ it reduces to DNLS equation and preserves ... 
Resonance solitons as black holes in Madelung fluid
Pashaev, Oktay; Lee, Jyh Hao (World Scientific Publishing, 200208)Envelope 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 ... 
Resonant dispersive Benney and BroerKaup systems in 2+1 dimensions
Lee, Jyh Hao; Pashaev, Oktay (IOP Publishing, 2014)We represent the Benney system of dispersionless hydrodynamic equations as NLS type infinite system of equations with quantum potential. We show that negative dispersive deformation of this system is an integrable system ... 
Selfdual ChernSimons solitons and quantum potential
Pashaev, Oktay; Lee, Jyh Hao (World Scientific Publishing, 200102)An influence of the quantum potential on the ChernSimons 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 ... 
Selfdual vortices in ChernSimons hydrodynamics
Lee, Jyh Hao; Pashaev, Oktay (Springer, 200106)The classical theory of a nonrelativistic charged particle interacting with a U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de BroglieBohm nonlinear quantum potential. The model is gauge ... 
Shock waves, chiral solitons and semiclassical limit of onedimensional anyons
Lee, Jyh Hao; Lin, ChiKun; Pashaev, Oktay (Elsevier, 200401)This paper is devoted to the semiclassical limit of the onedimensional Schrödinger equation with current nonlinearity and Sobolev regularity, before shocks appear in the limit system. In this limit, the modified Euler ... 
Soliton resonances in a generalized nonlinear Schrödinger equation
Pashaev, Oktay; Lee, Jyh Hao; Rogers, Colin (IOP Publishing, 20081114)It is shown that a generalized nonlinear Schrödinger equation proposed by Malomed and Stenflo admits, for a specific range of parameters, resonant soliton interaction. The equation is transformed to the 'resonant' nonlinear ... 
Soliton resonances, black holes and madelung fluid
Pashaev, Oktay; Lee, Jyh Hao (World Scientific Publishing, 200102)The reactiondiffusion system realizing a particular gauge fixing condition of the JackiwTeitelboim gravity is represented as a coupled pair of Burgers equations with positive and negative viscosity. For acoustic metric ... 
Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method
Lee, Jyh Hao; Pashaev, Oktay (Springer, 200707)We use the Hirota bilinear approach to consider physically relevant soliton solutions of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions, recently proposed for describing uniaxial waves in ...