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TMF, 2001, Volume 129, Number 2, Pages 333–344 (Mi tmf540)  

This article is cited in 6 scientific papers (total in 6 papers)

Quantizing the KdV Equation

A. K. Pogrebkov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the quantization procedure for the Gardner–Zakharov–Faddeev and Magri brackets using the fermionic representation for the KdV field. In both cases, the corresponding Hamiltonians are sums of two well-defined operators. Each operator is bilinear and diagonal with respect to either fermion or boson (current) creation/annihilation operators. As a result, the quantization procedure needs no space cutoff and can be performed on the entire axis. In this approach, solitonic states appear in the Hilbert space, and soliton parameters become quantized. We also demonstrate that the dispersionless KdV equation is uniquely and explicitly solvable in the quantum case.

DOI: https://doi.org/10.4213/tmf540

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English version:
Theoretical and Mathematical Physics, 2001, 129:2, 1586–1595

Bibliographic databases:


Citation: A. K. Pogrebkov, “Quantizing the KdV Equation”, TMF, 129:2 (2001), 333–344; Theoret. and Math. Phys., 129:2 (2001), 1586–1595

Citation in format AMSBIB
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\paper Quantizing the KdV Equation
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\jour Theoret. and Math. Phys.
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\issue 2
\pages 1586--1595
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. K. Pogrebkov, “Boson-fermion correspondence and quantum integrable and dispersionless models”, Russian Math. Surveys, 58:5 (2003), 1003–1037  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Pogrebkov A.K., “Hierarchy of quantum explicitly solvable and integrable models”, Bilinear Integrable Systems: From Classical to Quatum, Continuous to Discrete, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 201, 2006, 231–244  mathscinet  zmath  isi
    3. Zarmi Ya., “Quantized representation of some nonlinear integrable evolution equations on the soliton sector”, Phys Rev E, 83:5, Part 2 (2011), 056606  crossref  adsnasa  isi  elib  scopus  scopus
    4. Zarmi Ya., “Nonlinear Quantum-Dynamical System Based on the Kadomtsev-Petviashvili II Equation”, J. Math. Phys., 54:6 (2013), 063515  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Pustilnik M. Matveev K.A., “Fate of Classical Solitons in One-Dimensional Quantum Systems”, Phys. Rev. B, 92:19 (2015), 195146  crossref  adsnasa  isi  scopus  scopus
    6. Sotiriadis S., “Equilibration in One-Dimensional Quantum Hydrodynamic Systems”, J. Phys. A-Math. Theor., 50:42 (2017), 424004  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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