School of Mathematics

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Dr Vincent Caudrelier

Applied Mathematics

Contact details

Room: 9.304
Tel: +44 (0)113 3439522
Email: v.caudrelier @


Classical and quantum integrable systems
Classical and quantum inverse scattering method
Soliton equations
Boundaries and defects
Integrable PDEs on graphs
Yang-Baxter and reflection equations
Poisson-Lie groups and quantum groups

Research interests

I am interested in the area of Mathematical Physics known as integrable systems. They appear in all sorts of areas: classical and quantum mechanics, classical and quantum field theory, statistical mechanics, and in various forms: evolutionary models over discrete, semi-discrete or continuous spacetime or non-evolutionary. They share common features that are encapsulated in rich and important mathematical structures like Poisson-Lie groups, for classical integrable (field) theories and quantum groups, for quantum integrable (field) theories. The most famous equation related to these structures is the Yang-Baxter equation (classical or quantum).

They allow for exact solutions which have many applications in predicting exactly the physical behaviour of the systems they describe. For instance, correlation functions in quantum spin chains or long-time asymptotics of solutions of integrable PDEs can computed analytically and exactly. Typical domains of application are condensed matter physics, nonlinear waves dynamics in optics, fluid mechanics or plasma physics, 2D statistical models for percolation, etc.

My particular focus is on the study of the effect of boundaries and/or defects/impurities on solutions of these models. Recently, I have developed a scheme to formulate the inverse scattering method for integrable PDEs on (star) graphs.

Useful links

Personal webpage


Avan J, Caudrelier V On the origin of dual Lax pairs and their r-matrix structure Journal of Geometry and Physics, 120, 106-128, 2017
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Caudrelier V, Doyon B The quench map in an integrable classical field theory: nonlinear Schrödinger equation Journal of Physics A: Mathematical and Theoretical, 49, 2016
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Avan J, Caudrelier V, Doikou A, Kundu A Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality Nuclear Physics B, 902, 415-439, 2016
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Caudrelier V On the Inverse Scattering Method for Integrable PDEs on a Star Graph Communications in Mathematical Physics, 338, 893-917, 2015
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Caudrelier V Multisymplectic approach to integrable defects in the sine-Gordon model Journal of Physics A: Mathematical and Theoretical, 48, 1-23, 2015
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Caudrelier V, Kundu A A multisymplectic approach to defects in integrable classical field theory Journal of High Energy Physics, 2015
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Caudrelier V, Mintchev M, Ragoucy E Exact scattering matrix of graphs in magnetic field and quantum noise Journal of Mathematical Physics, 55, 083524-083524, 2014
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Caudrelier V, Zhang QC Yang–Baxter and reflection maps from vector solitons with a boundary Nonlinearity, 27, 1081-1103, 2014
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Caudrelier V, Crampé N, Zhang QC Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency SIGMA, 10, 2014
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Caudrelier V, Mintchev M, Ragoucy E Quantum wire network with magnetic flux Physics Letters A, 2013

Caudrelier V, Crampe N, Zhang QC Set-theoretical reflection equation: Classification of reflection maps J. Phys. A: Math. Theor., 46, 095203-095203, 2012
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Caudrelier V, Zhang QC Vector Nonlinear Schrödinger Equation on the half-line J. Phys. A: Math. Theor., 45, 105201-105201, 2011
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Caudrelier V, Ragoucy E Direct computation of scattering matrices for general quantum graphs Nucl.Phys.B, 828, 515-535, 2009
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Caudrelier V, Crampe N Symmetries of Spin Calogero Models Symmetry, Integrability and Geometry : Methods and Applications, 4, 2008

Caudrelier V On a systematic approach to defects in classical integrable field theories IJGMMP, 5, 1085-1108, 2007
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Caudrelier V, Crampe N Exact energy spectrum for models with equally spaced point potentials Nucl.Phys. B, 738, 351-367, 2005
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Caudrelier V Factorization in integrable systems with impurityCzechoslovak Journal of Physics 2005
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Caudrelier V, Mintchev M, Ragoucy E Solving the quantum nonlinear Schrodinger equation with delta-type impurity J MATH PHYS, 46, 2005

Caudrelier V, Crampe N Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity Rev.Math.Phys., 19, 349-370, 2005
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Caudrelier V, Mintchev M, Ragoucy E, Sorba P Reflection-Transmission Quantum Yang-Baxter Equations J.Phys. A, 38, 3431-3442, 2004
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Caudrelier V, Ragoucy E Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect J.Phys. A, 38, 2241-2258, 2004
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Caudrelier V, Mintchev M, Ragoucy E The quantum non-linear Schrodinger model with point-like defect J.Phys. A, 37, L367-L376, 2004
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Caudrelier V, Ragoucy E Lax pair and super-Yangian symmetry of the nonlinear super-Schrodinger equation J MATH PHYS, 44, 5706-5732, 2003

Caudrelier V, Crampe N Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry J.Phys.A, 37, 6285-6298, 2003
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Caudrelier V, Ragoucy E Quantum resolution of the nonlinear super-Schrodinger equation Int.J.Mod.Phys. A, 19, 1559-1578, 2003
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Caudrelier V Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application Studies in Applied Mathematics
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