Memoirs of the American Mathematical Society 1998; 216 pp; softcover Volume: 131 ISBN10: 0821806912 ISBN13: 9780821806913 List Price: US$63 Individual Members: US$37.80 Institutional Members: US$50.40 Order Code: MEMO/131/624
 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 RiemannHilbert 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 IWKB
 Appendix II
 Bibliography
