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Black holes and solitons of the quantized dispersionless NLS and DNLS equations

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Date
2002-07
Author
Pashaev, Oktay
Lee, Jyh Hao
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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
Collections
  • Mathematics / Matematik [528]
  • Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection [3276]
  • WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection [2953]


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