(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions
Share this pageFritz Gesztesy; Roman Svirsky
Using commutation methods, the authors present a general formalism to construct Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) \(N\)-soliton solutions relative to arbitrary (m)KdV background solutions. As an illustration of these techniques, the authors combine them with algebro-geometric methods and Hirota's \(\tau\)-function approach to systematically derive the (m)KdV \(N\)-soliton solutions on quasi-periodic finite-gap backgrounds.
Table of Contents
Table of Contents
(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions
- Contents vii8 free
- Abstract viii9 free
- 1. Introduction 110 free
- Acknowledgements 817 free
- 2. Quasi-Periodic Finite-Gap (m)KdV-Solutions 918
- 3. (m)KdV-Soliton Solutions on Quasi-Periodic Finite-Gap Backgrounds. I. The Single Commutation Method 1827
- 4. (m)KdV-Soliton Solutions on Quasi-Periodic Finite-Gap Backgrounds. II. The Double Commutation Method 2433
- Appendix A. Single Commutation Methods 3544
- Appendix B. Double Commutation Methods 4453
- Appendix C. Lax Pairs, r-Functions and Bäcklund Transformations 5766
- Appendix D. (m) KdV-Soliton Solutions Relative to General Backgrounds 6372
- Appendix E. Hyperelliptic Curves and Theta Functions 7483
- References 8392