Electronic ISBN:  9781470402136 
Product Code:  MEMO/131/624.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $37.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 131; 1998; 216 ppMSC: Primary 58;
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.
ReadershipGraduate students and research mathematicians working in completely integrable systems.

Table of Contents

Chapters

1. Introduction

2. Analysis of log formula

3. An example

4. Monotone initial data

5. Shock 1

6. Shock 2

7. Shock 3

8. Shock 4

9. Symmetric data

10. Global description

11. Large time calculations

12. Appendix I  WKB

13. Appendix II


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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.
Graduate students and research mathematicians working in completely integrable systems.

Chapters

1. Introduction

2. Analysis of log formula

3. An example

4. Monotone initial data

5. Shock 1

6. Shock 2

7. Shock 3

8. Shock 4

9. Symmetric data

10. Global description

11. Large time calculations

12. Appendix I  WKB

13. Appendix II