Quantization of the Kadomtsev–Petviashvili equation

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JournalTheoretical and Mathematical Physics
DateAccepted/In press - 26 Jul 2016
DatePublished (current) - 5 Sep 2017
Issue number2
Volume192
Number of pages22
Pages (from-to)1162–1183
Original languageEnglish

Abstract

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.

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    Research areas

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

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