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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 2, Pages 333–344
DOI: https://doi.org/10.4213/tmf540
(Mi tmf540)
 

This article is cited in 9 scientific papers (total in 9 papers)

Quantizing the KdV Equation

A. K. Pogrebkov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (218 kB) Citations (9)
References:
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.
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 2, Pages 1586–1595
DOI: https://doi.org/10.1023/A:1012895426139
Bibliographic databases:
Document Type: Article
Language: Russian
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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\pages 333--344
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\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 129
\issue 2
\pages 1586--1595
\crossref{https://doi.org/10.1023/A:1012895426139}
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Linking options:
  • https://www.mathnet.ru/eng/tmf540
  • https://doi.org/10.4213/tmf540
  • https://www.mathnet.ru/eng/tmf/v129/i2/p333
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:554
    Full-text PDF :240
    References:83
    First page:3
     
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