The discrete nonlinear Schrödinger equation: mathematical analysis, numerical computations and physical perspectives
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Springer tracts in modern physics
232 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 415 S. Ill., graph. Darst. |
| ISBN: | 9783540891994 3540891986 9783540891987 |
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| 245 | 1 | 0 | |a The discrete nonlinear Schrödinger equation |b mathematical analysis, numerical computations and physical perspectives |c Panayotis G. Kevrekidis |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS PART I GENERAL THEORY 1 GENERAL INTRODUCTION AND DERIVATION OF
THE DNLS EQUATION 3 1.1 GENERAL INTRODUCTION 3 1.2 PROTOTYPICAL
DERIVATION OF THE DNLS 4 REFERENCES 8 2 THE ONE-DIMENSIONAL CASE 11 2.1
SINGLE-PULSE SOLITARY WAVES 11 2.1.1 THE CONTINUUM APPROACH 11 2.1.2 THE
ANTI-CONTINUUM APPROACH 27 2.1.3 THE VARIATIONAL APPROACH 30 2.2
MULTIPULSE SOLITARY WAVES 34 2.2.1 MULTIPULSES NEAR THE ANTI-CONTINUUM
LIMIT 34 2.2.2 A DIFFERENT APPROACH: PERTURBED HAMILTONIAN SYSTEMS .. 41
2.2.3 MULTIPULSES CLOSE TO THE CONTINUUM LIMIT 48 REFERENCES 52 3 THE
TWO-DIMENSIONAL CASE 55 3.1 GENERAL NOTIONS 55 3.2 SINGLE-PULSE SOLITARY
WAVES 56 3.3 MULTIPULSES AND DISCRETE VORTICES 60 3.3.1 FORMULATION OF
THE BIFURCATION PROBLEM NEAR 6=0 60 3.3.2 PERSISTENCE OF DISCRETE
SOLUTIONS 63 3.3.3 STABILITY OF DISCRETE SOLUTIONS 74 3.3.4 NUMERICAL
RESULTS 83 REFERENCES 98 4 THE THREE-DIMENSIONAL CASE 99 4.1 GENERAL
THEORY 100 4.2 DISCRETE SOLITONS AND VORTICES 107 REFERENCES 116
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/993291317 DIGITALISIERT
DURCH CONTENTS THE DEFOCUSING CASE 117 5.1 DARK SOLITARY WAVES 118 5.1.1
THEORETICAL ANALYSIS 118 5.1.2 NUMERICAL RESULTS 125 5.2 VORTEX STATES
ON A NON-ZERO BACKGROUND 128 5.3 GAP STATES 131 5.3.1 GENERAL
TERMINOLOGY 132 5.3.2 DIPOLE CONFIGURATIONS 133 5.3.3 QUADRUPOLE
CONFIGURATIONS 136 5.3.4 VORTEX CONFIGURATION 138 5.3.5 GENERAL
PRINCIPLES DERIVED FROM STABILITY CONSIDERATIONS 140 REFERENCES 140
EXTENDED SOLUTIONS AND MODULATIONAL INSTABILITY 143 6.1 CONTINUUM
MODULATIONAL INSTABILITY 143 6.2 DISCRETE MODULATIONAL INSTABILITY 145
6.3 SOME CASE EXAMPLES 150 REFERENCES 152 MULTICOMPONENT DNLS EQUATIONS
153 7.1 LINEARLY COUPLED 153 7.2 NONLINEARLY COUPLED 158 7.2.1 ONE
DIMENSION 159 7.2.2 HIGHER DIMENSIONS 167 REFERENCES 170 PART II SPECIAL
TOPICS 8 EXPERIMENTAL RESULTS RELATED TO DNLS EQUATIONS 175 MASON A.
PORTER 8.1 INTRODUCTION 175 8.2 OPTICS 176 8.2.1 OPTICAL WAVEGUIDE
ARRAYS 176 8.2.2 PHOTOREFRACTIVE CRYSTALS 179 8.3 BOSE-EINSTEIN
CONDENSATION 182 8.4 SUMMARY AND OUTLOOK 186 REFERENCES 187 9 NUMERICAL
METHODS FOR DNLS 191 KODY J.H. LAW AND PANAYOTIS G. KEVREKIDIS 9.
CONTENTS 9.3 NUMERICAL COMPUTATIONS USING SPARSE MATRICES/ITERATIVE
SOLVERS . 199 9.4 CONCLUSIONS 203 REFERENCES 203 10 THE DYNAMICS OF
UNSTABLE WAVES 205 KODY J.H. LAW AND Q. ENAM HOQ 10.1 INTRODUCTION 205
10.2 STANDARD SCENARIO 206 10.2.1 1(+1)-DIMENSIONAL SOLUTIONS 206 10.2.2
2(+L)-DIMENSIONAL SOLUTIONS 208 10.2.3 3(+1 )-DIMENSIONAL SOLUTIONS 211
10.3 NON-STANDARD SCENARIO 213 10.3.1 HEXAGONAL LATTICE 213 10.3.2
DEFOCUSING NONLINEARITY 214 10.4 CONCLUSION AND FUTURE CHALLENGES 219
REFERENCES 219 11 A MAP APPROACH TO STATIONARY SOLUTIONS OF THE DNLS
EQUATION 221 RICARDO CARRETERO-GONZALEZ 11.1 INTRODUCTION 221 11.2 THE
2D MAP APPROACH FOR ID NONLINEAR LATTICES 222 11.3 ORBIT PROPERTIES AND
DIVERSITY IN THE DNLS 223 11.3.1 SYMMETRIES AND PROPERTIES OF THE CUBIC
DNLS STEADY STATES 224 11.3.2 HOMOGENEOUS, PERIODIC, MODULATED, AND
SPATIALLY CHAOTIC STEADY STATES 224 11.3.3 SPATIALLY LOCALIZED
SOLUTIONS: SOLITONS AND MULTIBREATHERS 226 11.4 BIFURCATIONS: THE ROAD
FROM THE ANTI-CONTINUOUS TO THE CONTINUOUS LIMIT 230 11.5 SUMMARY AND
FUTURE CHALLENGES 231 REFERENCES 232 12 FORMATION OF LOCALIZED MODES IN
DNLS 235 PANAYOTIS G. KEVREKIDIS 12.1 INTRODUCTION 235 12.2 THRESHOLD
CONDITIONS FOR THE INTEGRABLE NLS MODELS 236 12.2. XIV CONTENTS 13
FEW-LATTICE-SITE SYSTEMS OF DISCRETE SELF-TRAPPING EQUATIONS 249 HADI
SUSANTO 13.1 INTRODUCTION 249 13.2 INTEGRABILITY 251 13.3 CHAOS 254 13.4
APPLICATIONS AND EXPERIMENTAL OBSERVATIONS 254 13.5 CONCLUSIONS 256
REFERENCES 256 14 SURFACE WAVES AND BOUNDARY EFFECTS IN DNLS EQUATIONS
259 YING-JI HE AND BORIS A. MALOMED 14.1 INTRODUCTION 259 14.2 DISCRETE
NONLINEAR SCHROEDINGER EQUATIONS FOR SURFACE WAVES 260 14.2.1 THE
ONE-DIMENSIONAL SETTING 260 14.2.2 THE TWO-DIMENSIONAL SETTING 261
14.2.3 THE THREE-DIMENSIONAL SETTING 261 14.3 THEORETICAL INVESTIGATION
OF DISCRETE SURFACE WAVES 262 14.3.1 STABLE DISCRETE SURFACE SOLITONS IN
ONE DIMENSION 262 14.3.2 DISCRETE SURFACE SOLITONS AT AN INTERFACE
BETWEEN SELF-DEFOCUSING AND SELF-FOCUSING LATTICE MEDIA 264 14.3.3 TAMM
OSCILLATIONS OF UNSTAGGERED AND STAGGERED SOLITONS 265 14.3.4 DISCRETE
SURFACE SOLITONS IN TWO DIMENSIONS 267 14.3.5 SPATIOTEMPORAL DISCRETE
SURFACE SOLITONS 268 14.3.6 FINITE LATTICES AND THE METHOD OF IMAGES 268
14.4 EXPERIMENTAL RESULTS 270 14.4.1 DISCRETE SURFACE SOLITONS IN ONE
DIMENSION 270 14.4.2 STAGGERED MODES 270 14.4.3 DISCRETE SURFACE
SOLITONS IN TWO DIMENSIONS 271 14.5 CONCLUSIONS 273 REFERENCES 274 15
DISCRETE NONLINEAR SCHROEDINGER EQUATIONS WITH TIME-DEPENDENT
COEFFICIENTS (MANAGEMENT CONTENTS XV 16 EXCEPTIONAL DISCRETIZATIONS OF
THE NLS: EXACT SOLUTIONS AND CONSERVATION LAWS 293 SERGEY V. DMITRIEV
AND AVINASH KHARE 16.1 INTRODUCTION 293 16.2 REVIEW OF EXISTING WORKS
293 16.2.1 STATIONARY TRANSLATIONALLY INVARIANT SOLUTIONS 294 16.2.2
EXACT MOVING SOLUTIONS TO DNLS 297 16.3 CUBIC NONLINEARITY 297 16.3.1
CONSERVATION LAWS 298 16.3.2 TWO-POINT MAPS FOR STATIONARY SOLUTIONS 300
16.3.3 MOVING PULSE, KINK, AND SINE SOLUTIONS 303 16.3.4 STATIONARY TI
SOLUTIONS 304 16.3.5 MOVING BRIGHT SOLITONS 306 16.4 CONCLUSIONS AND
FUTURE CHALLENGES 308 REFERENCES 308 17 SOLITARY WAVE COLLISIONS 311
SERGEY V. DMITRIEV AND DIMITRI J. FRANTZESKAKIS 17.1 INTRODUCTION AND
SETUP 311 17.2 COLLISIONS IN THE WEAKLY DISCRETE NLS EQUATION 312 17.3
COLLISIONS IN THE STRONGLY DISCRETE NLS EQUATION 315 17.4 STRONGLY
DISCRETE NEARLY INTEGRABLE CASE 318 17.5 ROLE OF SOLITON S INTERNAL
MODES 320 17.6 SOLITARY WAVE COLLISIONS IN PHYSICALLY RELEVANT SETTINGS
322 17.7 CONCLUSIONS 324 17.8 FUTURE CHALLENGES 325 REFERENCES 326 18
RELATED MODELS 329 BORIS A. MALOMED 18.1 MODELS BEYOND THE STANDARD ONE
329 INTRODUCTION 329 ANISOTROPIE INTER-SITE COUPLINGS 330 NONCUBIC
ON-SITE NONLINEARITIES 330 NONLOCAL COUPLING 332 THE COMPETITION BETWEEN
ON-SITE AND INTER-SITE NONLINEARITIE XVI CONTENTS 18.4 SOLITONS IN THE
SALERNO MODEL WITH COMPETING INTER-SITE AND ON-SITE NONLINEARITIES 340
18.4.1 THE ID MODEL 340 18.4.2 THE 2D MODEL 343 18.5 ONE-DIMENSIONAL
SOLITONS IN THE SEMIDISCRETE SYSTEM WITH THE X (2) NONLINEARITY 346 18.6
CONCLUSION AND PERSPECTIVES 347 REFERENCES 349 19 DNLS WITH IMPURITIES
353 JESUS CUEVAS AND FAUSTINO PALMERO 19.1 INTRODUCTION 353 19.2
STATIONARY SOLUTIONS 354 19.2.1 LINEAR MODES 355 19.2.2 BIFURCATIONS 356
19.2.3 INVARIANT MANIFOLD APPROXIMATION 357 19.3 INTERACTION OF A MOVING
SOLITON WITH A SINGLE IMPURITY 360 19.4 COMPARISON WITH OTHER RELATED
MODELS 365 19.4.1 NONLINEAR IMPURITIES 365 19.4.2 COMPARISON WITH
KLEIN-GORDON BREATHERS 366 19.5 SUMMARY AND FUTURE CHALLENGES 366
REFERENCES 367 20 STATISTICAL MECHANICS OF DNLS 369 PANAYOTIS G.
KEVREKIDIS 20.1 INTRODUCTION 369 20.2 THEORETICAL RESULTS 370 20.3
RECENT RESULTS 374 REFERENCES 377 21 TRAVELING SOLITARY WAVES IN DNLS
EQUATIONS 379 ALAN R. CHAMPNEYS, VASSILIS M. ROTHOS AND THOMAS R.O.
MELVIN 21.1 INTRODUCTION 379 21.2 MATHEMATICAL FORMULATION 381 21.2.1
SPATIAL DYNAMICS FORMULATION 382 21.2.2 CENTER MANIFOLD REDUCTION 385
21.2.3 NORMAL FORM EQUATIONS NEAR THE ZERO-DISPERSION POINT . 387 21.2.
CONTENTS XVII 21.4 CONCLUSION 397 REFERENCES 398 22 DECAY AND STRICHARTZ
ESTIMATES FOR DNLS 401 ATANAS STEFANOV 22.1 INTRODUCTION 401 22.2 DECAY
AND STRICHARTZ ESTIMATES FOR THE DISCRETE SCHROEDINGER AND KLEIN-GORDON
EQUATION 403 22.2.1 A SPECTRAL RESULT FOR DISCRETE SCHROEDINGER OPERATORS
.... 405 22.2.2 APPLICATION TO EXCITATION THRESHOLDS 406 22.3 DECAY AND
STRICHARTZ ESTIMATES FOR THE DISCRETE SCHROEDINGER EQUATION PERTURBED BY
A POTENTIAL 407 22.3.1 SPECTRAL THEORETIC RESULTS FOR 1D SCHROEDINGER
OPERATORS . 410 22.4 CHALLENGES AND OPEN PROBLEMS 410 22.4.1 DOES WEAK
COUPLING ALLOW EIGENVALUES IN THREE DIMENSIONS? 410 22.4.2 CLR-TYPE
BOUNDS FOR DISCRETE SCHROEDINGER OPERATORS AND RELATED ISSUES 411 22.4.3
SHOW ANALOGS OF THEOREMS 8, 9, 10 IN HIGHER DIMENSIONS 411 22.4.4
ASYMPTOTIC STABILITY AND NUCLEATION 411 REFERENCES 412 INDEX 413
|
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| id | DE-604.BV035347552 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:49Z |
| institution | BVB |
| isbn | 9783540891994 3540891986 9783540891987 |
| language | English |
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| owner_facet | DE-703 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| physical | XX, 415 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Springer tracts in modern physics |
| series2 | Springer tracts in modern physics |
| spelling | Kevrekidis, Panayotis G. Verfasser (DE-588)1079877339 aut The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives Panayotis G. Kevrekidis Berlin [u.a.] Springer 2009 XX, 415 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer tracts in modern physics 232 Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Gittermodell (DE-588)4226961-1 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Gittermodell (DE-588)4226961-1 s DE-604 Springer tracts in modern physics 232 (DE-604)BV000000153 232 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151754&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kevrekidis, Panayotis G. The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives Springer tracts in modern physics Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Gittermodell (DE-588)4226961-1 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4226961-1 |
| title | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives |
| title_auth | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives |
| title_exact_search | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives |
| title_full | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives Panayotis G. Kevrekidis |
| title_fullStr | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives Panayotis G. Kevrekidis |
| title_full_unstemmed | The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives Panayotis G. Kevrekidis |
| title_short | The discrete nonlinear Schrödinger equation |
| title_sort | the discrete nonlinear schrodinger equation mathematical analysis numerical computations and physical perspectives |
| title_sub | mathematical analysis, numerical computations and physical perspectives |
| topic | Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Gittermodell (DE-588)4226961-1 gnd |
| topic_facet | Nichtlineare Schrödinger-Gleichung Gittermodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151754&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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