Integrable deformations of coupled σ-models

Marginal β deformations of [Formula: see text] super-Yang–Mills theory are known to correspond to a certain class of deformations of the S5 background subspace of type IIB string theory in AdS5×S5. An analogous set of deformations of the AdS5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equations, suggesting that the twisted string theory is classically integrable in this regime. These Bethe equations can be derived algorithmically by relying on the existence of Lax representations, and on the Riemann–Hilbert interpretation of the thermodynamic Bethe ansatz. This letter is a review of a seminar given at the Institute for Advanced Study, based on research completed in collaboration with McLoughlin.

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Cauchy problems related to integrable deformations of pseudo differential operators

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2014.05.004 ◽

2014 ◽

Vol 85 ◽

pp. 196-205 ◽

Cited By ~ 6

Author(s):

G.F. Helminck ◽

A.G. Helminck ◽

E.A. Panasenko

Keyword(s):

Differential Operators ◽

Cauchy Problems ◽

Pseudo Differential Operators ◽

Integrable Deformations

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Appendix 1. Moduli spaces of meromorphic connections, quiver varieties, and integrable deformations

Mathematical Society of Japan Memoirs - 4-dimensional Painlevé-type equations ◽

10.2969/msjmemoirs/03701c030 ◽

2018 ◽

pp. 113-153 ◽

Cited By ~ 1

Author(s):

Kazuki Hiroe

Keyword(s):

Moduli Spaces ◽

Quiver Varieties ◽

Integrable Deformations ◽

Meromorphic Connections

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Induced surfaces and their integrable deformations

Bäcklund and Darboux Transformations. The Geometry of Solitons - CRM Proceedings and Lecture Notes ◽

10.1090/crmp/029/25 ◽

2001 ◽

pp. 281-289

Author(s):

B. Konopelchenko ◽

G. Landolfi

Keyword(s):

Integrable Deformations

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Doubled aspects of generalised dualities and integrable deformations

Journal of High Energy Physics ◽

10.1007/jhep02(2019)189 ◽

2019 ◽

Vol 2019 (2) ◽

Cited By ~ 23

Author(s):

Saskia Demulder ◽

Falk Hassler ◽

Daniel C. Thompson

Keyword(s):

Integrable Deformations

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Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500592 ◽

2019 ◽

Vol 16 (04) ◽

pp. 1950059 ◽

Cited By ~ 2

Author(s):

Kaiyin Huang ◽

Shaoyun Shi ◽

Zhiguo Xu

Keyword(s):

Galois Groups ◽

Point Of View ◽

Integrable Case ◽

Analytic First Integrals ◽

Rikitake System ◽

Constants Of Motion ◽

Integrable Deformations ◽

Particular Solution ◽

Almost All ◽

Parameter Values

The aim of this paper is to investigate a generalized Rikitake system from the integrability point of view. For the integrable case, we derive a family of integrable deformations of the generalized Rikitake system by altering its constants of motion, and give two classes of Hamilton–Poisson structures which implies these integrable deformations, including the generalized Rikitake system, are bi-Hamiltonian and have infinitely many Hamilton–Poisson realizations. By analyzing properties of the differential Galois groups of normal variational equations (NVEs) along certain particular solution, we show that the generalized Rikitake system is not rationally integrable in an extended Liouville sense for almost all parameter values, which is in accord with the fact that this system admits chaotic behaviors for a large range of its parameters. The non-existence of analytic first integrals are also discussed.

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On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

ITM Web of Conferences ◽

10.1051/itmconf/20192901015 ◽

2019 ◽

Vol 29 ◽

pp. 01015 ◽

Cited By ~ 1

Author(s):

Cristian Lăzureanu ◽

Ciprian Hedrea ◽

Camelia Petrişor

Keyword(s):

Incompressible Fluid ◽

Mechanical System ◽

Integrable Systems ◽

Degrees Of Freedom ◽

Mechanical Systems ◽

Ideal Incompressible Fluid ◽

First Integrals ◽

Integrable Deformation ◽

Integrable Deformations ◽

The Given

Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maximally superintegrable Hamiltonian mechanical system that describes the motion of two vortices in an ideal incompressible fluid, and we show that some of these integrable deformations are Hamiltonian mechanical systems too.

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