Quantization of the Kadomtsev–Petviashvili equation

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We propose a quantization of the Kadomtsev–Petviashvili equation on a cylinder equivalent to an infinite system of nonrelativistic one-dimensional bosons with the masses m = 1, 2,.. The Hamiltonian is Galilei-invariant and includes the split and merge termsΨm1†Ψm2†Ψm1+m2andΨm1+m2†Ψm1Ψm2for all combinations of particles with masses m 1, m 2, and m 1 + m 2for a special choice of coupling constants. We construct the Bethe eigenfunctions for the model and verify the consistency of the coordinate Bethe ansatz and hence the quantum integrability of the model up to the mass M=8 sector.

Original languageEnglish
Pages (from-to)1162–1183
Number of pages22
JournalTheoretical and Mathematical Physics
Issue number2
Publication statusPublished - 5 Sept 2017

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  • Bethe ansatz
  • Kadomtsev–Petviashvili equation
  • integrable model
  • quantization

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