6 Integrable nonlinear equations

Kapitel in diesem Buch

1. Frontmatter i
2. Preface vii
3. Notation ix
4. Contents xi
5. 0 Introduction 1
6. 1 Preliminaries 13
7. 2 Self-adjoint Dirac system: rectangular matrix potentials 44
8. 3 Skew-self-adjoint Dirac system: rectangular matrix potentials 79
9. 4 Linear system auxiliary to the nonlinear optics equation 101
10. 5 Discrete systems 126
11. 6 Integrable nonlinear equations 177
12. 7 General GBDT theorems and explicit solutions of nonlinear equations 210
13. 8 Some further results on inverse problems and generalized Bäcklund-Darboux transformation (GBDT) 230
14. 9 Sliding inverse problems for radial Dirac and Schrödinger equations 242
15. Appendices
16. A General-type canonical system: pseudospectral and Weyl functions 267
17. B Mathematical system theory 304
18. C Krein’s system 306
19. D Operator identities corresponding to inverse problems 308
20. E Some basic theorems 320
21. Bibliography 323
22. Index 339