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

Published online by Cambridge University Press:  17 February 2009

Oktay K. Pashaev  and
Jyh-Hao Lee
Oktay K. Pashaev
Affiliation:
Department of Mathematics, Izmir Institute of Technology, Liyla-Izmir, 35437Turkey; e-mail: pashaev@likya.iyte.edu.tr. Joint Institute for Nuclear Research, Dubna, 141980, Russian Federation. Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan, ROC; e-mail: leejh@math.sinica.edu.tw.
Jyh-Hao Lee
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan, ROC; e-mail: leejh@math.sinica.edu.tw.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 73 - 81
Copyright
Copyright © Australian Mathematical Society 2002

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