Quantizing the KdV equation

A. K. Pogrebkov

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1586-1595
Number of pages10
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - Nov 2001


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