| Introduction / 1： |
| Integrable dynamical systems / 2： |
| Synopsis of integrable systems / 2.1： |
| Algebraic methods / 4： |
| The Liouville theorem / 5： |
| Analytical methods |
| The closed Toda chain / 2.3： |
| Action-angle variables |
| The Calogero-Moser model / 7： |
| Lax pairs / 8： |
| Isomonodromic deformations |
| Grassmannian and integrable hierarchies / 2.5： |
| Existence of an r-matrix |
| The KP hierarchy / 10： |
| Commuting flows / 11： |
| The KdV hierarchy |
| The Toda field theories / 2.7： |
| The Kepler problem |
| Classical inverse scattering method / 13： |
| The Euler top / 14： |
| Symplectic geometry |
| Riemann surfaces / 2.9： |
| The Lagrange top |
| Lie algebras / 16： |
| Index |
| The Kowalevski top |
| The Neumann model / 2.11： |
| Geodesics on an ellipsoid / 2.12： |
| Separation of variables in the Neumann model / 2.13： |
| Examples of Lax pairs with spectral parameter / 3.1： |
| The Zakharov-Shabat construction / 3.2： |
| Coadjoint orbits and Hamiltonian formalism / 3.3： |
| Elementary flows and wave function / 3.4： |
| Factorization problem / 3.5： |
| Tau-functions / 3.6： |
| Integrable field theories and monodromy matrix / 3.7： |
| Abelianization / 3.8： |
| Poisson brackets of the monodromy matrix / 3.9： |
| The group of dressing transformations / 3.10： |
| Soliton solutions / 3.11： |
| The classical and modified Yang-Baxter equations / 4.1： |
| Algebraic meaning of the classical Yang-Baxter equations / 4.2： |
| Adler-Kostant-Symes scheme / 4.3： |
| Construction of integrable systems / 4.4： |
| Solving by factorization / 4.5： |
| The open Toda chain / 4.6： |
| The r-matrix of the Toda models / 4.7： |
| Solution of the open Toda chain / 4.8： |
| Toda system and Hamiltonian reduction / 4.9： |
| The Lax pair of the Kowalevski top / 4.10： |
| The spectral curve / 5.1： |
| The eigenvector bundle / 5.2： |
| The adjoint linear system / 5.3： |
| Time evolution / 5.4： |
| Theta-functions formulae / 5.5： |
| Baker-Akhiezer functions / 5.6： |
| Linearization and the factorization problem / 5.7： |
| Symplectic form / 5.8： |
| Separation of variables and the spectral curve / 5.10： |
| Riemann surfaces and integrability / 5.11： |
| Infinite-dimensional systems / 5.13： |
| The model / 6.1： |
| The eigenvectors / 6.2： |
| Reconstruction formula / 6.4： |
| Symplectic structure / 6.5： |
| The Sklyanin approach / 6.6： |
| The Poisson brackets / 6.7： |
| Reality conditions / 6.8： |
| The spin Calogero-Moser model / 7.1： |
| Lax pair / 7.2： |
| The r-matrix / 7.3： |
| The scalar Calogero-Moser model / 7.4： |
| Reconstruction formulae / 7.5： |
| Poles systems and double-Bloch condition / 7.9： |
| Hitchin systems / 7.11： |
| Examples of Hitchin systems / 7.12： |
| The trigonometric Calogero-Moser model / 7.13： |
| Monodromy data / 8.1： |
| Isomonodromy and the Riemann-Hilbert problem / 8.3： |
| Schlesinger transformations / 8.4： |
| Ricatti equation / 8.6： |
| Sato's formula / 8.8： |
| The Hirota equations / 8.9： |
| Tau-functions and theta-functions / 8.10： |
| The Painleve equations / 8.11： |
| Fermions and GL [infinity] / 9.1： |
| Boson-fermion correspondence / 9.3： |
| Tau-functions and Hirota bilinear identities / 9.4： |
| The KP hierarchy and its soliton solutions / 9.5： |
| Fermions and Grassmannians / 9.6： |
| Schur polynomials / 9.7： |
| From fermions to pseudo-differential operators / 9.8： |
| The Segal-Wilson approach / 9.9： |
| The algebra of pseudo-differential operators / 10.1： |
| The Baker-Akhiezer function of KP / 10.2： |
| Algebro-geometric solutions of KP / 10.4： |
| The tau-function of KP / 10.5： |
| The generalized KdV equations / 10.6： |
| KdV Hamiltonian structures / 10.7： |
| Bihamiltonian structure / 10.8： |
| The Drinfeld-Sokolov reduction / 10.9： |
| Whitham equations / 10.10： |
| Solution of the Whitham equations / 10.11： |
| The KdV equation / 11.1： |
| Hamiltonian structures and Virasoro algebra / 11.2： |
| Algebro-geometric solutions / 11.4： |
| Finite-zone solutions / 11.6： |
| Analytical description of solitons / 11.7： |
| Local fields / 11.9： |
| Whitham's equations / 11.10： |
| The Liouville equation / 12.1： |
| The Toda systems and their zero-curvature representations / 12.2： |
| Solution of the Toda field equations / 12.3： |
| Hamiltonian formalism / 12.4： |
| Conformal structure / 12.5： |
| Dressing transformations / 12.6： |
| The affine sinh-Gordon model / 12.7： |
| Dressing transformations and soliton solutions / 12.8： |
| N-soliton dynamics / 12.9： |
| The sine-Gordon equation / 12.10： |
| The Jost solutions / 13.2： |
| Inverse scattering as a Riemann-Hilbert problem / 13.3： |
| Time evolution of the scattering data / 13.4： |
| The Gelfand-Levitan-Marchenko equation / 13.5： |
| Poisson brackets of the scattering data / 13.6： |
| Poisson manifolds and symplectic manifolds / 13.8： |
| Coadjoint orbits / 14.2： |
| Symmetries and Hamiltonian reduction / 14.3： |
| The case M = T*G / 14.4： |
| Poisson-Lie groups / 14.5： |
| Action of a Poisson-Lie group on a symplectic manifold / 14.6： |
| The groups G and G* / 14.7： |
| Smooth algebraic curves / 14.8： |
| Hyperelliptic curves / 15.2： |
| The Riemann-Hurwitz formula / 15.3： |
| The field of meromorphic functions of a Riemann surface / 15.4： |
| Line bundles on a Riemann surface / 15.5： |
| Divisors / 15.6： |
| Chern class / 15.7： |
| Serre duality / 15.8： |
| The Riemann-Roch theorem / 15.9： |
| Abelian differentials / 15.10： |
| Riemann bilinear identities / 15.11： |
| Jacobi variety / 15.12： |
| Theta-functions / 15.13： |
| The genus 1 case / 15.14： |
| The Riemann-Hilbert factorization problem / 15.15： |
| Lie groups and Lie algebras / 16.1： |
| Semi-simple Lie algebras / 16.2： |
| Linear representations / 16.3： |
| Real Lie algebras / 16.4： |
| Affine Kac-Moody algebras / 16.5： |
| Vertex operator representations / 16.6： |
| Introduction / 1： |
| Integrable dynamical systems / 2： |
| Synopsis of integrable systems / 2.1： |
図書
