A Continuum Limit of the Toda Lattice
Seiten
1998
American Mathematical Society (Verlag)
978-0-8218-0691-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0691-3 (ISBN)
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Using the integrability of the finite Toda lattice, this title adapts 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. It also makes extensive use of techniques from the theory of Riemann-Hilbert problems.
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.
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.
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.
| Erscheint lt. Verlag | 1.6.1998 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 411 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-8218-0691-2 / 0821806912 |
| ISBN-13 | 978-0-8218-0691-3 / 9780821806913 |
| Zustand | Neuware |
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