Book contents
- Frontmatter
- Dedication
- Contents
- 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∆E
- 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
10 - Similarity reductions of integrable P∆Es
Published online by Cambridge University Press: 05 September 2016
Book contents
- Frontmatter
- Dedication
- Contents
- 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∆E
- 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
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- Discrete Systems and Integrability , pp. 280 - 303Publisher: Cambridge University PressPrint publication year: 2016