Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4646
Title: Black holes and solitons of the quantized dispersionless NLS and DNLS equations
Authors: Pashaev, Oktay
Lee, Jyh Hao
Pashaev, Oktay
Izmir Institute of Technology. Mathematics
Keywords: Schrödinger equation
Dynamics
Quantum potential
Hirota bilinear form
Issue Date: Jul-2002
Publisher: Cambridge University Press
Source: Pashaev, O., and Lee, J. H. (2002). Black holes and solitons of the quantized dispersionless NLS and DNLS equations. ANZIAM Journal, 44(1), 73-81. doi:10.1017/S1446181100007926
Abstract: The classical dynamics of non-relativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of the potential strength, recovers the standard Schrödinger equation. In addition, the classically forbidden region corresponds to the Planck constant analytically continued to pure imaginary, values. We apply the same procedure to the NLS and DNLS equations, constructing first the corresponding dispersionless limits and then adding quantum deformations. All these deformations admit the Lax representation as well as the Hirota bilinear form. In the classically forbidden region we find soliton resonances and black hole phenomena. For deformed DNLS the chiral solitons with single event horizon and resonance dynamics are constructed.
URI: http://doi.org/10.1017/S1446181100007926
http://hdl.handle.net/11147/4646
ISSN: 1446-1811
1446-1811
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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