Introduction to Classical Integrable Systems: Contents

  title={Introduction to Classical Integrable Systems: Contents},
  author={Olivier Babelon and Denis Bernard and Michel Talon},
published by the press syndicate of the university of cambridge 

On the Symmetries of Classical String Theory

I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrumgenerating symmetries of classical string theory.

Triangular reductions of the 2D toda hierarchy

New reductions of the 2D Toda equations associated with lower-triangular difference operators are proposed. Their explicit Hamiltonian description is obtained.

Classical and Stochastic Löwner–Kufarev Equations

In this paper we present a historical and scientific account of the development of the theory of the Lowner–Kufarev classical and stochastic equations spanning the 90-year period from the seminal

On the quantum inverse problem for the closed Toda chain

We reconstruct the canonical operators pi, qi of the quantum closed Toda chain in terms of Sklyanin's separated variables.

On the r-matrix structure of the hyperbolic BC(n) Sutherland model

Working in a symplectic reduction framework, we construct a dynamical r-matrix for the classical hyperbolic BC(n) Sutherland model with three independent coupling constants. We also examine the Lax

Differential algebra of the Painlevé property

In the 1970s, self-similar solutions to integrable PDEs were found to satisfy the Painlevé condition. There ensued a proposal to linearize the Painlevé condition via inverse scattering, which

Classical Integrable and Separable Hamiltonian Systems

  • M. Błaszak
  • Mathematics
    Quantum versus Classical Mechanics and Integrability Problems
  • 2019
In this chapter we introduce the concept of classical integrability of Hamiltonian systems and then develop the separability theory of such systems based on the notion of separation relations


Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The

Quantum integrability of quadratic Killing tensors

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a “minimal” quantization scheme,

Painlevé Tests, Singularity Structure and Integrability

After a brief introduction to the Painleve property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as