Spectral methods in soliton equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman
1994
|
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
73 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 394 S. |
| ISBN: | 058223963X |
Internformat
MARC
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| 100 | 1 | |a Iliev, Iliya D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spectral methods in soliton equations |c I. D. Iliev; E. Kh. Khristov and K. P. Kirchev |
| 264 | 1 | |a Harlow |b Longman |c 1994 | |
| 300 | |a 394 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 73 | |
| 700 | 1 | |a Khristov, Evgeni K. |e Verfasser |4 aut | |
| 700 | 1 | |a Kirchev, Kiril P. |e Verfasser |4 aut | |
| 830 | 0 | |a Pitman monographs and surveys in pure and applied mathematics |v 73 |w (DE-604)BV000022446 |9 73 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-019641678 | ||
Datensatz im Suchindex
| _version_ | 1804142003455262720 |
|---|---|
| adam_text | Table of Contents
Preface jx
Introduction. Summary of the Main Ideas and Results 1
Chapter 1. Spectral Theory of the Regular A-Operators
1.1 Introduction 25
1.2 Expansions in products of solutions of two Sturm-Liouville problems . 29
1.3 Uniqueness theorems in the inverse problem. Perturbation theory for
the spectral data 40
1.4 Explicit solutions of inverse problems. Continuous analog of Newton s
method 47
1.5 The inverse periodic Sturm-Liouville problem 61
1.6 Operator Aa and its resolvent 68
1.7 On the Hamiltonian theory for the KdV equation in the periodic case 78
1.8 Expansions in products of solutions of two Dirac systems 84
1.9 A-operators associated with Dirac systems 98
LA Appendix: Wronskian relations and Aa-operators 104
l.B Appendix: Differential properties of the Crum transformation and
applications 107
Comments and bibliographical directions 112
Chapter 2. Spectral Theory for A-Operators on the Semi-axis
2.1 The direct and inverse scattering problems. The Gel fand-Levitan-
Marchenko equation 114
2.2 The inverse scattering problem as an evolution equation 119
2.3 Expansions in products of solutions of two radial Schrodinger
equations 124
2.4 A-operators 136
2.5 Perturbation theory for the scattering data 141
2.6 The expansion formula in Povzner-Levitan and Levin s representations 150
vi Table of contents
2.7 Continuous analog of Newton s method in the inverse scattering
problem I 160
2.8 Continuous analog of Newton s method in the inverse scattering
problem II 168
2.9 Expansions in the case of higher orbital momenta 176
2.10 A-operators for general boundary conditions 181
2.11 A-operators for the Dirac system. Spectral theory and applications .. 186
2. A Appendix: Gavurin s theory of the continuous analog of Newton s
method 193
Comments and bibliographical directions 196
Chapter 3. A-Operators on the Line and Nonlinear Evolution Equations
3.1 The direct and inverse scattering problems for the Schrodinger equation
on the line 198
3.2 Expansions in products of solutions of two Schrodinger equations .... 202
3.3 Operators A± and applications 205
3.4 Symplectic expansion formulas and Lagrangian manifolds 211
3.5 Inverse scattering transform for the KdV equation 219
3.6 Expansions in products of solutions of two Dirac systems 226
3.7 Spectral theory of A-operators related to products of solutions
of two Dirac systems 235
3.8 Symplectic expansions for a Dirac system and associated operators .. 239
3.9 Nonlinear evolution equations solvable by 1ST for a Dirac system .... 242
3.10 Spectral properties of a Schrodinger equation with energy-dependent
potential generating completely integrable Hamiltonian systems 248
3.11 Cauchy problem for the linearization of a nonlinear evolution equation 263
3. A Appendix: Remarks on gauge transformations in ISM 275
3.B Appendix: Geometry of the recursion operators 284
Comments and bibliographical directions 297
Chapter 4. Stability of Solitary Wave Solutions for Nonlinear Evolution
Equations
4.1 Mathematical background on stability in infinite-dimensional spaces . 300
4.2 Solitary waves of one-dimensional singular Schrodinger equations.
Stable cases 306
4.3 Unstable cases 318
4.4 Stable traveling wave solutions of the generalized KdV and BBM
equations 324
4.5 Unstable traveling wave solutions of the generalized KdV and BBM
equations 333
4.6 Stability of the single-soliton solution of the complex MKdV equation 348
Table of contents vii
4.7 Examples of stable and unstable solitary waves 357
4. A Appendix: Remarks on the Cauchy problem for nonlinear evolution
equations 363
Bibliography 369
|
| any_adam_object | 1 |
| author | Iliev, Iliya D. Khristov, Evgeni K. Kirchev, Kiril P. |
| author_facet | Iliev, Iliya D. Khristov, Evgeni K. Kirchev, Kiril P. |
| author_role | aut aut aut |
| author_sort | Iliev, Iliya D. |
| author_variant | i d i id idi e k k ek ekk k p k kp kpk |
| building | Verbundindex |
| bvnumber | BV024974097 |
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| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024974097 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:24:51Z |
| institution | BVB |
| isbn | 058223963X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019641678 |
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| owner_facet | DE-11 DE-188 |
| physical | 394 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Longman |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Iliev, Iliya D. Verfasser aut Spectral methods in soliton equations I. D. Iliev; E. Kh. Khristov and K. P. Kirchev Harlow Longman 1994 394 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 73 Khristov, Evgeni K. Verfasser aut Kirchev, Kiril P. Verfasser aut Pitman monographs and surveys in pure and applied mathematics 73 (DE-604)BV000022446 73 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iliev, Iliya D. Khristov, Evgeni K. Kirchev, Kiril P. Spectral methods in soliton equations Pitman monographs and surveys in pure and applied mathematics |
| title | Spectral methods in soliton equations |
| title_auth | Spectral methods in soliton equations |
| title_exact_search | Spectral methods in soliton equations |
| title_full | Spectral methods in soliton equations I. D. Iliev; E. Kh. Khristov and K. P. Kirchev |
| title_fullStr | Spectral methods in soliton equations I. D. Iliev; E. Kh. Khristov and K. P. Kirchev |
| title_full_unstemmed | Spectral methods in soliton equations I. D. Iliev; E. Kh. Khristov and K. P. Kirchev |
| title_short | Spectral methods in soliton equations |
| title_sort | spectral methods in soliton equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
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