ANZIAM  J.  44 (2002), 73-81
Black holes and solitons of the quantized dispersionless NLS and DNLS equations

Oktay K. Pashaev
  Department of Mathematics
  Izmir Institute of Technology
  35437 Turkey
Jyh-Hao Lee
  Institute of Mathematics
  Academia Sinica
  Taipei 11529

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.
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