Quantization of the Kadomtsev–Petviashvili equation

Karol Kozlowski; Evgeny Sklyanin; Alessandro Torrielli

doi:10.1134/S0040577917080074

Quantization of the Kadomtsev–Petviashvili equation

Karol Kozlowski, Evgeny Sklyanin, Alessandro Torrielli

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1162–1183
Number of pages	22
Journal	Theoretical and Mathematical Physics
Volume	192
Issue number	2
DOIs	https://doi.org/10.1134/S0040577917080074
Publication status	Published - 5 Sept 2017

Bibliographical note

© 2017 Pleiades Publishing, Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Keywords

Bethe ansatz
Kadomtsev–Petviashvili equation
integrable model
quantization

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10.1134/S0040577917080074

1607.07685v1-1
© 2017 Pleiades Publishing, Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 257 KB

https://arxiv.org/abs/1607.07685

Cite this

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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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N2 - 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.

AB - 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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Quantization of the Kadomtsev–Petviashvili equation

Abstract

Bibliographical note

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Evgeny Sklyanin, FRS

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Quantization of the Kadomtsev–Petviashvili equation

Abstract

Bibliographical note

Keywords

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Evgeny Sklyanin, FRS

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