In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A novel feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.

Readership

Graduate students and research mathematicians working in completely integrable systems.

Table of Contents

• Introduction
• Analysis of Log formula
• An example
• Monotone initial data
• Shock 1
• Shock 2
• Shock 3
• Shock 4
• Symmetric data
• Global description
• Large time calculations
• Appendix I--WKB
• Appendix II
• Bibliography