| Preface |
| Preface to the English Edition |
| What is a Backlund Transformation? / Chapter 1.： |
| Hamiltonian representation of P[subscript II] / 1.1.： |
| Immediately accessible solutions / 1.2.： |
| Backlund transformations / 1.3.： |
| Composing Backlund transformations / 1.4.： |
| Generating solutions / 1.5.： |
| Picture of classical solutions / 1.6.： |
| The Symmetric Form / Chapter 2.： |
| The symmetric form of P[subscript IV] / 2.1.： |
| Fundamental special solutions / 2.2.： |
| Affine Weyl group / 2.3.： |
| The symmetric form of P[subscript II] / 2.4.： |
| [tau]-Functions / Chapter 3.： |
| Poisson structure and the Hamiltonian system / 3.1.： |
| [tau]-Functions and their differential equations / 3.2.： |
| Backlund transformations of the [tau]-functions / 3.3.： |
| Various relations among the [tau]-functions / 3.4.： |
| [tau]-Functions for P[subscript II] / 3.5.： |
| [tau]-Functions on the Lattice / Chapter 4.： |
| The lattice for P[subscript II] / 4.1.： |
| The lattice for P[subscript IV] / 4.2.： |
| [phi]-Factors and Okamoto polynomials / 4.3.： |
| Discrete system of type A[superscript (1) subscript n-1] / 4.4.： |
| [tau]-Functions on the A[subscript n-1] lattice / 4.5.： |
| Jacobi-Trudi Formula / Chapter 5.： |
| Young diagrams and Maya diagrams / 5.1.： |
| Formulas of Jacobi-Trudi type / 5.2.： |
| Examples of P[subscript IV] and P[subscript II] / 5.3.： |
| Schur functions and [phi]-factors / 5.4.： |
| Getting Familiar with Determinants / Chapter 6.： |
| Basic properties of minor determinants / 6.1.： |
| Gauss decomposition and the Jacobi identity / 6.2.： |
| Diagonalization of triangular matrices / 6.3.： |
| Plucker relations / 6.4.： |
| Gauss Decomposition and Birational Transformations / Chapter 7.： |
| Birational transformation of the f variables / 7.1.： |
| Birational transformations arising from the Gauss decomposition / 7.2.： |
| Where are the [tau]-functions? / 7.3.： |
| Explicit formulas of Jacobi-Trudi type / 7.4.： |
| Birational transformations of type A[subscript infinity] and of type A[superscript (1) subscript n-1] / 7.5.： |
| Action of the affine Weyl group on the Maya diagrams / 7.6.： |
| Lax Formalism / Chapter 8.： |
| Relation with linear ordinary differential equations / 8.1.： |
| Symmetric forms of P[subscript II], P[subscript IV] and the Lax representations / 8.2.： |
| Appendix |
| Profile of Painleve equations / A.0.： |
| Hamiltonian systems [Section 1.1] / A.1.： |
| Poisson structure and canonical transformations [Section 1.1] / A.2.： |
| Riccati equations [Section 1.2] / A.3.： |
| Computation of Backlund transformations [Sections 1.5 and 2.3] / A.4.： |
| Classical solutions and invariant divisors [Sections 1.6 and 2.2] / A.5.： |
| Semidirect product of groups [Section 2.3] / A.6.： |
| Cartan matrices and Dynkin diagrams [Section 2.3] / A.7.： |
| Demazure operators [Section 2.5] / A.8.： |
| Hirota's bilinear operators [Section 3.2] / A.9.： |
| Application of the exterior algebra [Sections 6.1 and 6.4] / A.10.： |
| Bibliography |
| Index |
| Preface |
| Preface to the English Edition |
| What is a Backlund Transformation? / Chapter 1.： |
図書
図書
