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A Continuum Limit of the Toda Lattice

P. Deift New York University-Courant Institute of Mathematical Sciences, New York, NY
K. T-R McLaughlin Ohio State University, Columbus, OH
Available Formats:
Electronic ISBN: 978-1-4704-0213-6
Product Code: MEMO/131/624.E
List Price: $63.00 MAA Member Price:$56.70
AMS Member Price: $37.80 Click above image for expanded view A Continuum Limit of the Toda Lattice P. Deift New York University-Courant Institute of Mathematical Sciences, New York, NY K. T-R McLaughlin Ohio State University, Columbus, OH Available Formats:  Electronic ISBN: 978-1-4704-0213-6 Product Code: MEMO/131/624.E  List Price:$63.00 MAA Member Price: $56.70 AMS Member Price:$37.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1311998; 216 pp
MSC: 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 Riemann-Hilbert 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
• Requests

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Volume: 1311998; 216 pp
MSC: 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 Riemann-Hilbert 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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