Theory of solitons: the inverse scattering method
Saved in:
| Format: | Book |
|---|---|
| Language: | English Russian |
| Published: |
New York u.a.
Consultants Bureau
1984
|
| Series: | Contemporary Soviet mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XI, 276 S. |
| ISBN: | 0306109778 |
Staff View
MARC
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| 130 | 0 | |a Teorija solitonov | |
| 245 | 1 | 0 | |a Theory of solitons |b the inverse scattering method |c S. Novikov ... |
| 264 | 1 | |a New York u.a. |b Consultants Bureau |c 1984 | |
| 300 | |a XI, 276 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Contemporary Soviet mathematics | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Scattering (Mathematics) | |
| 650 | 4 | |a Solitons | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverse Streutheorie |0 (DE-588)4561758-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
Contents
Introduction: Weak Nonlinearity and Dispersion 1
CHAPTER I
THE INVERSE SCATTERING METHOD 11
1 Elements of the Scattering Theory. The Inverse Problem
in the Quantum Theory of Scattering 12
2 Integration of the KdV by the Inverse Scattering Method 23
3 Reflectionless Potentials and N Soliton Solutions 26
4 The KdV as a Hamiltonian System 32
5 Polynomial Integrals of Motion 35
6 Complete Integrability of the KdV. Higher Order KdV 37
7 Differential Difference Systems 45
8 Nonlinear Schrodinger Equation and Sine Gordon Equation 57
9 Inverse Scattering Problem for a System of Two
Differential Equations 61
10 Nonlinear Schrodinger Equation 68
11 The Sine Gordon Equation 79
CHAPTER II
PERIODIC SOLUTIONS OF THE KdV EQUATION 91
1 Schrodinger Equation with a Periodic Potential.
Periodic Analog of the Gardner Greene Kruskal
Miura (GGKM) Equation 91
2 Stationary Problem for Higher Order KdV. Exact
Solutions of the KdV 97
3 Stationary Solutions of Higher Order KdV and the
Potentials of a Schrodinger Equation with a
Finite Number of Bands. Riemann Surfaces 104
4 Analytical Properties of the Bloch Eigenfunction
of a Finite Gap Potential on a Riemann Surface 108
5 Some Applications 112
ix
x CONTENTS
6 Elements of the Theory of Riemann Surfaces , Cycles on
Riemann Surface 120
7 Differentials on Riemann Surfaces. Abelian
(Holomorphic) Differentials and Differentials
with Poles 130
8 The Bloch Eigenfuntion and Quasi Momentum. Associated
Differentials on the Riemann Surface and Their
Dynamics 138
9 Exact Expressions for Finite Gap Potentials and
Solutions of the KdV 146
10 Certain Particular Solutions of the KdV 149
CHAPTER III
CONSTRUCTION OF INTEGRABLE SYSTEMS AND THEIR
SOLUTIONS: MODERN METHODS 154
1 Regular Riemann Problem 154
2 Riemann Problem with Zeros 157
3 The Inverse Scattering Problem for a First Order
Matrix System 163
4 The N Wave Problem 174
5 Soliton Solutions 180
6 Systems Integrable by Riemann Problem Technique 184
7 Relativistic Invariant Systems Chiral Fields 189
CHAPTER IV
ASYMPTOTIC SOLUTIONS OVER LARGE TIMES 205
1 Integral Relationships. Nonlinear Fraunhofer
Diffraction 206
2 Explicit Expressions of Asymptotic Forms (the
Nonlinear SchrSdinger Equation) 210
3 Explicit Expressions of Asymptotic Forms (the KdV
Equation) 215
4 The Whitham Averaging Method 219
APPENDIX
THE THEORY OF KADOMTSEV PETVIASHVILI EQUATION
(TWO DIMENSIONAL KdV). CERTAIN DISCRETE SYSTEMS 240
1 Certain Integrable Two Dimensional Systems 240
2 Conservation Laws 244
3 The Dressing Method 245
4 Soliton Like Solutions of the KP 248
5 Exact Solutions Dependent on Functional Parameters 251
6 Riemann Surface Technique. Finite Gap Solutions of
Rank 1 253
CONTENTS xi
7 Rational Solutions of the KP. Discrete Systems of
Particles on a Line 256
8 The Method of Holomorphic Vector Bundles Over Riemann
Surfaces. Functional Parameters in Exact
Solutions 259
9 Certain Remarks on the Periodic Toda Lattice 265
REFERENCES 269
INDEX 273 |
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| author_GND | (DE-588)118786490 |
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| ctrlnum | (OCoLC)10071941 (DE-599)BVBBV000299093 |
| dewey-full | 515.3/55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/55 |
| dewey-search | 515.3/55 |
| dewey-sort | 3515.3 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-20T05:55:14Z |
| institution | BVB |
| isbn | 0306109778 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000182414 |
| oclc_num | 10071941 |
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| physical | XI, 276 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Consultants Bureau |
| record_format | marc |
| series2 | Contemporary Soviet mathematics |
| spelling | Teorija solitonov Theory of solitons the inverse scattering method S. Novikov ... New York u.a. Consultants Bureau 1984 XI, 276 S. txt rdacontent n rdamedia nc rdacarrier Contemporary Soviet mathematics Aus d. Russ. übers. Inverse problems (Differential equations) Scattering (Mathematics) Solitons Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Inverse Streutheorie (DE-588)4561758-2 gnd rswk-swf Streutheorie (DE-588)4183697-2 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Soliton (DE-588)4135213-0 s Inverse Streutheorie (DE-588)4561758-2 s DE-604 Streutheorie (DE-588)4183697-2 s Differentialgleichung (DE-588)4012249-9 s Novikov, Sergej P. 1938-2024 Sonstige (DE-588)118786490 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000182414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theory of solitons the inverse scattering method Inverse problems (Differential equations) Scattering (Mathematics) Solitons Differentialgleichung (DE-588)4012249-9 gnd Inverse Streutheorie (DE-588)4561758-2 gnd Streutheorie (DE-588)4183697-2 gnd Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4561758-2 (DE-588)4183697-2 (DE-588)4135213-0 |
| title | Theory of solitons the inverse scattering method |
| title_alt | Teorija solitonov |
| title_auth | Theory of solitons the inverse scattering method |
| title_exact_search | Theory of solitons the inverse scattering method |
| title_full | Theory of solitons the inverse scattering method S. Novikov ... |
| title_fullStr | Theory of solitons the inverse scattering method S. Novikov ... |
| title_full_unstemmed | Theory of solitons the inverse scattering method S. Novikov ... |
| title_short | Theory of solitons |
| title_sort | theory of solitons the inverse scattering method |
| title_sub | the inverse scattering method |
| topic | Inverse problems (Differential equations) Scattering (Mathematics) Solitons Differentialgleichung (DE-588)4012249-9 gnd Inverse Streutheorie (DE-588)4561758-2 gnd Streutheorie (DE-588)4183697-2 gnd Soliton (DE-588)4135213-0 gnd |
| topic_facet | Inverse problems (Differential equations) Scattering (Mathematics) Solitons Differentialgleichung Inverse Streutheorie Streutheorie Soliton |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000182414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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