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Discrete Systems and Integrability

J. Hietarinta, N. Joshi, and F. W. Nijhoff
Publisher: 
Cambridge University Press
Publication Date: 
2017
Number of Pages: 
445
Format: 
Paperback
Series: 
Cambridge Texts in Applied Mathematics
Price: 
49.99
ISBN: 
9781107669482
Category: 
Monograph
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Preface
1. Introduction to difference equations
2. Discrete equations from transformations of continuous equations
3. Integrability of P∆Es
4. Interlude: lattice equations and numerical algorithms
5. Continuum limits of lattice P∆Es
6. One-dimensional lattices and maps
7. Identifying integrable difference equations
8. Hirota's bilinear method
9. Multi-soliton solutions and the Cauchy matrix scheme
10. Similarity reductions of integrable P∆Es
11. Discrete Painlevé equations
12. Lagrangian multiform theory
Appendix A. Elementary difference calculus and difference equations
Appendix B. Theta functions and elliptic functions
Appendix C. The continuous Painlevé equations and the Garnier system
Appendix D. Some determinantal identities
References
Index.