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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)
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DOI: https://doi.org/10.4213/tmf540
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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    • This publication is cited in the following 9 articles:
    1. Maged Marghany, Synthetic Aperture Radar Image Processing Algorithms for Nonlinear Oceanic Turbulence and Front Modeling, 2024, 119  crossref
    2. Bastianello A., Alba V., Caux J.-S., “Generalized Hydrodynamics With Space-Time Inhomogeneous Interactions”, Phys. Rev. Lett., 123:13 (2019), 130602  crossref  mathscinet  isi  scopus
    3. Sotiriadis S., “Equilibration in One-Dimensional Quantum Hydrodynamic Systems”, J. Phys. A-Math. Theor., 50:42 (2017), 424004  crossref  mathscinet  zmath  isi  scopus  scopus
    4. 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
    5. 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
    6. 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
    7. 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
    8. A.K. Pogrebkov, NATO Science Series, 201, Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete, 2006, 231  crossref
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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