Theoretical and Mathematical Physics

, Volume 129, Issue 2, pp 1586–1595 | Cite as

Quantizing the KdV Equation

  • A. K. Pogrebkov


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.


Soliton Hilbert Space Quantum Case Quantization Procedure Fermionic Representation 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. K. Pogrebkov
    • 1
  1. 1.Steklov Mathematical Institute, RASMoscowRussia

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