Nonlinear waves and solitons on contours and closed surfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2007
|
| Schriftenreihe: | Springer complexity
Springer Series in synergetics |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 453 - 460 |
| Beschreibung: | XIX, 464 S. graph. Darst. |
| ISBN: | 9783540728726 3540728724 |
Internformat
MARC
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| 100 | 1 | |a Ludu, Andrei |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear waves and solitons on contours and closed surfaces |c Andrei Ludu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XIX, 464 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Springer complexity | |
| 490 | 0 | |a Springer Series in synergetics | |
| 500 | |a Literaturverz. S. 453 - 460 | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Compact spaces | |
| 650 | 4 | |a Nonlinear waves |x Mathematics | |
| 650 | 4 | |a Solitons |x Mathematics | |
| 650 | 0 | 7 | |a Soliton |0 (DE-588)4135213-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kompakter Raum |0 (DE-588)4164857-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137510532546560 |
|---|---|
| adam_text | ANDREI LUDU NONLINEAR WAVES AND SOLITONS ON CONTOURS AND CLOSED SURFACES
WITH 140 FIGURES SPRINGER CONTENTS PART I MATHEMATICAL PREREQUISITES 1
INTRODUCTION 5 1.1 INTRODUCTION TO SOLITON THEORY 5 1.2 ALGEBRAIC AND
GEOMETRIE APPROACHES 6 1.3 A LIST OF USEFUL DERIVATIVES 8 2 MATHEMATICAL
PREREQUISITES 11 2.1 ELEMENTS OF TOPOLOGY 11 2.1.1 SEPARATION AXIOMS 12
2.1.2 COMPACTNESS 15 2.1.3 WEIERSTRASS-STONE THEOREM 17 2.1.4
CONNECTEDNESS, CONNECTIVITY, AND HOMOTOPY 18 2.1.5 SEPARABILITY AND
BASIS 20 2.1.6 METRIE AND NORMED SPACES 20 2.2 ELEMENTS OF HOMOLOGY 21 3
THE IMPORTANCE OF THE BOUNDARY 23 3.1 THE POWER OF COMPACT BOUNDARIES:
REPRESENTATION FORMULAS 23 3.1.1 REPRESENTATION FORMULA FOR N = 1:
TAYLOR SERIES 24 3.1.2 REPRESENTATION FORMULA FOR N = 2: CAUCHY FORMULA
... 24 3.1.3 REPRESENTATION FORMULA FOR N = 3: GREEN FORMULA .... 25
3.1.4 REPRESENTATION FORMULA IN GENERAL: STOKES THEOREM . . 26 3.2
COMMENTS AND EXAMPLES 28 4 VECTOR FIELDS, DIFFERENTIAL FORMS, AND
DERIVATIVES 3 1 4.1 MANIFOLDS AND MAPS 32 4.2 DIFFERENTIAL AND VECTOR
FIELDS 35 4.3 EXISTENCE AND UNIQUENESS THEOREMS: DIFFERENTIAL EQUATION
APPROACH 39 XIII CONTENTS 4.4 EXISTENCE AND UNIQUENESS THEOREMS: FLOW
BOX APPROACH ... 45 4.5 COMPACT SUPPORTED VECTOR FIELDS 47 4.6 LIE
DERIVATIVE AND DIFFERENTIAL FORMS 47 4.7 INVARIANTS 52 4.8 FIBER BUNDLES
54 4.9 POINCARE LEMMA 57 4.10 TENSOR ANALYSIS, COVARIANT DERIVATIVE, AND
CONNECTIONS 58 4.11 THE MIXED COVARIANT DERIVATIVE 60 4.12 CURVILINEAR
ORTHOGONAL COORDINATES 62 4.12.1 GRADIENT 64 4.12.2 DIVERGENCE 64 4.12.3
CURL 65 4.12.4 LAPLACIAN 65 4.12.5 SPECIAL TWO-DIMENSIONAL NONLINEAR
ORTHOGONAL COORDINATES 66 4.13 PROBLEMS 67 GEOMETRY OF CURVES 69 5.1
ELEMENTS OF DIFFERENTIAL GEOMETRY OF CURVES 69 5.2 CLOSED CURVES 76 5.3
CURVES LYING ON A SURFACE 78 5.4 PROBLEMS 79 MOTION OF CURVES AND
SOLITONS 81 6.1 NONLINEAR KINEMATICS OF TWO-DIMENSIONAL CURVES AND
SOLITONS 82 6.1.1 THE TIME EVOLUTION OF LENGTH AND AREA IN GENERAL . .
94 6.2 KINEMATICS OF CURVE MOTION: THREE DIMENSION 101 6.3 PROBLEMS 102
GEOMETRY OF SURFACES 103 7.1 ELEMENTS OF DIFFERENTIAL GEOMETRY OF
SURFACES 105 7.2 COVARIANT DERIVATIVE AND CONNECTIONS 112 7.3 GEOMETRY
OF PARAMETRIZED SURFACES EMBEDDED IN R3 116 7.3.1 CHRISTOFFEL SYMBOLS
AND COVARIANT DIFFERENTIATION FOR HYBRID TENSORS 118 7.4 COMPACT
SURFACES 120 7.5 SURFACE DIFFERENTIAL OPERATORS 122 7.5.1 SURFACE
GRADIENT 123 7.5.2 SURFACE DIVERGENCE 125 7.5.3 SURFACE LAPLACIAN 126
7.5.4 SURFACE CURL 127 7.5.5 INTEGRAL RELATIONS FOR SURFACE DIFFERENTIAL
OPERATORS . . 129 7.5.6 APPLICATIONS 131 7.6 PROBLEMS 134 CONTENTS XV 8
THEORY OF MOTION OF SURFACES 137 8.1 COORDINATES AND VELOCITIES ON A
FLUID SURFACE 137 8.2 GEOMETRY OF MOVING SURFACES 143 8.3 DYNAMICS OF
MOVING SURFACES 145 8.4 BOUNDARY CONDITIONS FOR MOVING FLUID INTERFACES
148 8.5 DYNAMICS OF THE FLUID INTERFACES 149 8.6 PROBLEMS 151 PART II
SOLITONS AND NONLINEAR WAVES ON CLOSED CURVES AND SURFACES 9 KINEMATICS
OF HYDRODYNAMICS 157 9.1 LAGRANGIAN VS. EULERIAN FRAMES 157 9.1.1
INTRODUCTION 158 9.1.2 GEOMETRICAL PICTURE FOR LAGRANGIAN VS. EULERIAN
159 9.2 FLUID FIBER BUENDLE 161 9.2.1 INTRODUCTION 161 9.2.2 MOTIVATION
FOR A GEOMETRICAL APPROACH 164 9.2.3 THE FIBER BUENDLE 167 9.2.4 FIXED
FLUID CONTAINER 168 9.2.5 FREE SURFACE FIBER BUENDLE 172 9.2.6 HOW DOES
THE TIME DERIVATIVE OF TENSORS TRANSFORM FROM EULER TO LAGRANGE FRAME?
174 9.3 PATH LINES, STREAM LINES, AND PARTICLE CONTOURS 178 9.4
EULERIAN-LAGRANGIAN DESCRIPTION FOR MOVING CURVES 184 9.5 THE FREE
SURFACE 184 9.6 EQUATION OF CONTINUITY 186 9.6.1 INTRODUCTION 186 9.6.2
SOLUTIONS OF THE CONTINUITY EQUATION ON COMPACT INTERVALS 192 9.7
PROBLEMS 198 10 DYNAMICS OF HYDRODYNAMICS 201 10.1 MOMENTUM
CONSERVATION: EULER AND NAVIER-STOKES EQUATIONS 201 10.2 BOUNDARY
CONDITIONS 204 10.3 CIRCULATION THEOREM 206 10.4 SURFACE TENSION 212
10.4.1 PHYSICAL PROBLEM 212 10.4.2 MINIMAL SURFACES 214 10.4.3
APPLICATION 216 10.4.4 ISOTHERMAL PARAMETRIZATION 219 10.4.5 TOPOLOGICAL
PROPERTIES OF MINIMAL SURFACES 222 XVI CONTENTS 10.4.6 GENERAL CONDITION
FOR MINIMAL SURFACES 224 10.4.7 SURFACE TENSION FOR ALMOST ISOTHERMAL
PARAMETRIZATION 225 10.5 SPECIAL FLUIDS 228 10.6 REPRESENTATION THEOREMS
IN FLUID DYNAMICS 228 10.6.1 HELMHOLTZ DECOMPOSITION THEOREM IN R 3 228
10.6.2 DECOMPOSITION FORMULA FOR TRANSVERSAL ISOTROPIE VECTOR FIELDS 231
10.6.3 SOLENOIDAL-TOROIDAL DECOMPOSITION FORMULAS 234 10.7 PROBLEMS 234
11 NONLINEAR SURFACE WAVES IN ONE DIMENSION 237 11.1 KDV EQUATION
DEDUCTION FOR SHALLOW WATERS 237 11.2 SMOOTH TRANSITIONS BETWEEN
PERIODIC AND APERIODIC SOLUTIONS 242 11.3 MODIFIED KDV EQUATION AND
GENERALIZATIONS 246 11.4 HYDRODYNAMIC EQUATIONS INVOLVING HIGHER-ORDER
NONLINEARITIES 249 11.4.1 A COMPACT VERSION FOR KDV 249 11.4.2 SMALL
AMPLITUDE APPROXIMATION 252 11.4.3 DISPERSION RELATIONS 254 11.4.4 THE
FUELL EQUATION 255 11.4.5 REDUCTION OF GKDV TO OTHER EQUATIONS AND
SOLUTIONS 257 11.4.6 THE FINITE DIFFERENCE FORM 261 11.5 BOUSSINESQ
EQUATIONS ON A CIRCLE 264 12 NONLINEAR SURFACE WAVES IN TWO DIMENSIONS
267 12.1 GEOMETRY OF TWO-DIMENSIONAL FLOW 267 12.2 TWO-DIMENSIONAL
NONLINEAR EQUATIONS 275 12.3 TWO-DIMENSIONAL FLUID SYSTEMS WITH BOUNDARY
278 12.4 OSCILLATIONS IN TWO-DIMENSIONAL LIQUID DROPS 281 12.5 CONTOURS
DESCRIBED BY QUARTIC CLOSED CURVES 283 12.6 SURFACE NONLINEAR WAVES IN
TWO-DIMENSIONAL LIQUID NITROGEN DROPS 284 13 NONLINEAR SURFACE WAVES IN
THREE DIMENSIONS 289 13.1 OSCILLATIONS OF INVISCID DROPS: THE LINEAR
MODEL 291 13.1.1 DROP IMMERSED IN ANOTHER FLUID 293 13.1.2 DROP WITH
RIGID CORE 295 13.1.3 MOVING CORE 301 13.1.4 DROP VOLUME 305 13.2
OSCILLATIONS OF VISCOUS DROPS: THE LINEAR MODEL 307 13.2.1 MODEL 1 308
CONTENTS XVII 13.3 NONLINEAR THREE-DIMENSIONAL OSCILLATIONS OF
AXISYMMETRIC DROPS 322 13.3.1 NONLINEAR RESONANCES IN DROP OSCILLATION
330 13.4 OTHER NONLINEAR EFFECTS IN DROP OSCILLATIONS 340 13.5 SOLITONS
ON THE SURFACE OF LIQUID DROPS 344 13.6 PROBLEMS 353 14 OTHER SPECIAL
NONLINEAR COMPACT SYSTEMS 355 14.1 NONLINEAR COMPACT SHAPES AND
COLLECTIVE MOTION 355 14.2 THE HAMILTONIAN STRUCTURE FOR FREE BOUNDARY
PROBLEMS ON COMPACT SURFACES 359 PART III PHYSICAL NONLINEAR SYSTEMS AT
DIFFERENT SCALES 15 FILAMENTS, CHAINS, AND SOLITONS 367 15.1 VORTEX
FILAMENTS 367 15.1.1 GAS DYNAMICS FILAMENT MODEL AND SOLITONS 372 15.1.2
SPECIAL SOLUTIONS 375 15.1.3 INTEGRATION OF SERRET-FRENET EQUATIONS FOR
FILAMENTS . . 377 15.1.4 THE RICCATI FORM OF THE SERRET-FRENET EQUATIONS
380 15.1.5 SOLITON SOLUTIONS ON THE VORTEX FILAMENT 381 15.1.6 VORTEX
FILAMENTS AND THE NONLINEAR SCHROEDINGER EQUATION 384 15.2 NONLINEAR
DYNAMICS OF STIFF CHAINS 387 15.3 PROBLEMS 390 16 SOLITONS ON THE
BOUNDARIES OF MICROSCOPIC SYSTEMS 391 16.1 FIELD THEORY MODEL ON A
CLOSED CONTOUR AND INSTANTONS .... 392 16.1.1 QUANTIZATION: EXCITED
STATES 394 16.1.2 QUANTIZATION: INSTANTONS AND TUNNELING 394 16.2
CLUSTERS AS SOLITARY WAVES ON THE NUCLEAR SURFACE 396 16.3 SOLITONS AND
QUASIMOLECULAR STRUCTURE 404 16.4 SOLITON MODEL FOR HEAVY EMITTED
NUCLEAR CLUSTERS 406 16.4.1 QUINTIC NONLINEAR SCHROEDINGER EQUATION FOR
NUCLEAR CLUSTER DECAY 408 16.5 CONTOUR SOLITONS IN THE QUANTUM HALL
LIQUID 411 16.5.1 PERTURBATIVE APPROACH 414 16.5.2 GEOMETRIE APPROACH
417 17 NONLINEAR CONTOUR DYNAMICS IN MACROSCOPIC SYSTEMS .... 423 17.1
PLASMA VORTEX 423 17.1.1 EFFECTIVE SURFACE TENSION IN
MAGNETOHYDRODYNAMICS AND PLASMA SYSTEMS 423 17.1.2 TRAJECTORIES IN
MAGNETIC FIELD CONFIGURATIONS 424 17.1.3 MAGNETIC SURFACES IN STATIC
EQUILIBRIUM 433 XVIII CONTENTS 17.2 ELASTIC SPHERES 440 17.3 NONLINEAR
EVOLUTION OF OSCILLATION MODES IN NEUTRON STARS . . 441 18 MATHEMATICAL
ANNEX 445 18.1 DIFFERENTIABLE MANIFOLDS 445 18.2 RICCATI EQUATION 446
18.3 SPECIAL FUNCTIONS 446 18.4 ONE-SOLITON SOLUTIONS FOR THE KDV, MKDV,
AND THEIR COMBINATION 448 18.5 SCALING AND NONLINEAR DISPERSION
RELATIONS 450 REFERENCES 453 INDEX 461
|
| adam_txt |
ANDREI LUDU NONLINEAR WAVES AND SOLITONS ON CONTOURS AND CLOSED SURFACES
WITH 140 FIGURES SPRINGER CONTENTS PART I MATHEMATICAL PREREQUISITES 1
INTRODUCTION 5 1.1 INTRODUCTION TO SOLITON THEORY 5 1.2 ALGEBRAIC AND
GEOMETRIE APPROACHES 6 1.3 A LIST OF USEFUL DERIVATIVES 8 2 MATHEMATICAL
PREREQUISITES 11 2.1 ELEMENTS OF TOPOLOGY 11 2.1.1 SEPARATION AXIOMS 12
2.1.2 COMPACTNESS 15 2.1.3 WEIERSTRASS-STONE THEOREM 17 2.1.4
CONNECTEDNESS, CONNECTIVITY, AND HOMOTOPY 18 2.1.5 SEPARABILITY AND
BASIS 20 2.1.6 METRIE AND NORMED SPACES 20 2.2 ELEMENTS OF HOMOLOGY 21 3
THE IMPORTANCE OF THE BOUNDARY 23 3.1 THE POWER OF COMPACT BOUNDARIES:
REPRESENTATION FORMULAS 23 3.1.1 REPRESENTATION FORMULA FOR N = 1:
TAYLOR SERIES 24 3.1.2 REPRESENTATION FORMULA FOR N = 2: CAUCHY FORMULA
. 24 3.1.3 REPRESENTATION FORMULA FOR N = 3: GREEN FORMULA . 25
3.1.4 REPRESENTATION FORMULA IN GENERAL: STOKES THEOREM . . 26 3.2
COMMENTS AND EXAMPLES 28 4 VECTOR FIELDS, DIFFERENTIAL FORMS, AND
DERIVATIVES 3 1 4.1 MANIFOLDS AND MAPS 32 4.2 DIFFERENTIAL AND VECTOR
FIELDS 35 4.3 EXISTENCE AND UNIQUENESS THEOREMS: DIFFERENTIAL EQUATION
APPROACH 39 XIII CONTENTS 4.4 EXISTENCE AND UNIQUENESS THEOREMS: FLOW
BOX APPROACH . 45 4.5 COMPACT SUPPORTED VECTOR FIELDS 47 4.6 LIE
DERIVATIVE AND DIFFERENTIAL FORMS 47 4.7 INVARIANTS 52 4.8 FIBER BUNDLES
54 4.9 POINCARE LEMMA 57 4.10 TENSOR ANALYSIS, COVARIANT DERIVATIVE, AND
CONNECTIONS 58 4.11 THE MIXED COVARIANT DERIVATIVE 60 4.12 CURVILINEAR
ORTHOGONAL COORDINATES 62 4.12.1 GRADIENT 64 4.12.2 DIVERGENCE 64 4.12.3
CURL 65 4.12.4 LAPLACIAN 65 4.12.5 SPECIAL TWO-DIMENSIONAL NONLINEAR
ORTHOGONAL COORDINATES 66 4.13 PROBLEMS 67 GEOMETRY OF CURVES 69 5.1
ELEMENTS OF DIFFERENTIAL GEOMETRY OF CURVES 69 5.2 CLOSED CURVES 76 5.3
CURVES LYING ON A SURFACE 78 5.4 PROBLEMS 79 MOTION OF CURVES AND
SOLITONS 81 6.1 NONLINEAR KINEMATICS OF TWO-DIMENSIONAL CURVES AND
SOLITONS 82 6.1.1 THE TIME EVOLUTION OF LENGTH AND AREA IN GENERAL . .
94 6.2 KINEMATICS OF CURVE MOTION: THREE DIMENSION 101 6.3 PROBLEMS 102
GEOMETRY OF SURFACES 103 7.1 ELEMENTS OF DIFFERENTIAL GEOMETRY OF
SURFACES 105 7.2 COVARIANT DERIVATIVE AND CONNECTIONS 112 7.3 GEOMETRY
OF PARAMETRIZED SURFACES EMBEDDED IN R3 116 7.3.1 CHRISTOFFEL SYMBOLS
AND COVARIANT DIFFERENTIATION FOR HYBRID TENSORS 118 7.4 COMPACT
SURFACES 120 7.5 SURFACE DIFFERENTIAL OPERATORS 122 7.5.1 SURFACE
GRADIENT 123 7.5.2 SURFACE DIVERGENCE 125 7.5.3 SURFACE LAPLACIAN 126
7.5.4 SURFACE CURL 127 7.5.5 INTEGRAL RELATIONS FOR SURFACE DIFFERENTIAL
OPERATORS . . 129 7.5.6 APPLICATIONS 131 7.6 PROBLEMS 134 CONTENTS XV 8
THEORY OF MOTION OF SURFACES 137 8.1 COORDINATES AND VELOCITIES ON A
FLUID SURFACE 137 8.2 GEOMETRY OF MOVING SURFACES 143 8.3 DYNAMICS OF
MOVING SURFACES 145 8.4 BOUNDARY CONDITIONS FOR MOVING FLUID INTERFACES
148 8.5 DYNAMICS OF THE FLUID INTERFACES 149 8.6 PROBLEMS 151 PART II
SOLITONS AND NONLINEAR WAVES ON CLOSED CURVES AND SURFACES 9 KINEMATICS
OF HYDRODYNAMICS 157 9.1 LAGRANGIAN VS. EULERIAN FRAMES 157 9.1.1
INTRODUCTION 158 9.1.2 GEOMETRICAL PICTURE FOR LAGRANGIAN VS. EULERIAN
159 9.2 FLUID FIBER BUENDLE 161 9.2.1 INTRODUCTION 161 9.2.2 MOTIVATION
FOR A GEOMETRICAL APPROACH 164 9.2.3 THE FIBER BUENDLE 167 9.2.4 FIXED
FLUID CONTAINER 168 9.2.5 FREE SURFACE FIBER BUENDLE 172 9.2.6 HOW DOES
THE TIME DERIVATIVE OF TENSORS TRANSFORM FROM EULER TO LAGRANGE FRAME?
174 9.3 PATH LINES, STREAM LINES, AND PARTICLE CONTOURS 178 9.4
EULERIAN-LAGRANGIAN DESCRIPTION FOR MOVING CURVES 184 9.5 THE FREE
SURFACE 184 9.6 EQUATION OF CONTINUITY 186 9.6.1 INTRODUCTION 186 9.6.2
SOLUTIONS OF THE CONTINUITY EQUATION ON COMPACT INTERVALS 192 9.7
PROBLEMS 198 10 DYNAMICS OF HYDRODYNAMICS 201 10.1 MOMENTUM
CONSERVATION: EULER AND NAVIER-STOKES EQUATIONS 201 10.2 BOUNDARY
CONDITIONS 204 10.3 CIRCULATION THEOREM 206 10.4 SURFACE TENSION 212
10.4.1 PHYSICAL PROBLEM 212 10.4.2 MINIMAL SURFACES 214 10.4.3
APPLICATION 216 10.4.4 ISOTHERMAL PARAMETRIZATION 219 10.4.5 TOPOLOGICAL
PROPERTIES OF MINIMAL SURFACES 222 XVI CONTENTS 10.4.6 GENERAL CONDITION
FOR MINIMAL SURFACES 224 10.4.7 SURFACE TENSION FOR ALMOST ISOTHERMAL
PARAMETRIZATION 225 10.5 SPECIAL FLUIDS 228 10.6 REPRESENTATION THEOREMS
IN FLUID DYNAMICS 228 10.6.1 HELMHOLTZ DECOMPOSITION THEOREM IN R 3 228
10.6.2 DECOMPOSITION FORMULA FOR TRANSVERSAL ISOTROPIE VECTOR FIELDS 231
10.6.3 SOLENOIDAL-TOROIDAL DECOMPOSITION FORMULAS 234 10.7 PROBLEMS 234
11 NONLINEAR SURFACE WAVES IN ONE DIMENSION 237 11.1 KDV EQUATION
DEDUCTION FOR SHALLOW WATERS 237 11.2 SMOOTH TRANSITIONS BETWEEN
PERIODIC AND APERIODIC SOLUTIONS 242 11.3 MODIFIED KDV EQUATION AND
GENERALIZATIONS 246 11.4 HYDRODYNAMIC EQUATIONS INVOLVING HIGHER-ORDER
NONLINEARITIES 249 11.4.1 A COMPACT VERSION FOR KDV 249 11.4.2 SMALL
AMPLITUDE APPROXIMATION 252 11.4.3 DISPERSION RELATIONS 254 11.4.4 THE
FUELL EQUATION 255 11.4.5 REDUCTION OF GKDV TO OTHER EQUATIONS AND
SOLUTIONS 257 11.4.6 THE FINITE DIFFERENCE FORM 261 11.5 BOUSSINESQ
EQUATIONS ON A CIRCLE 264 12 NONLINEAR SURFACE WAVES IN TWO DIMENSIONS
267 12.1 GEOMETRY OF TWO-DIMENSIONAL FLOW 267 12.2 TWO-DIMENSIONAL
NONLINEAR EQUATIONS 275 12.3 TWO-DIMENSIONAL FLUID SYSTEMS WITH BOUNDARY
278 12.4 OSCILLATIONS IN TWO-DIMENSIONAL LIQUID DROPS 281 12.5 CONTOURS
DESCRIBED BY QUARTIC CLOSED CURVES 283 12.6 SURFACE NONLINEAR WAVES IN
TWO-DIMENSIONAL LIQUID NITROGEN DROPS 284 13 NONLINEAR SURFACE WAVES IN
THREE DIMENSIONS 289 13.1 OSCILLATIONS OF INVISCID DROPS: THE LINEAR
MODEL 291 13.1.1 DROP IMMERSED IN ANOTHER FLUID 293 13.1.2 DROP WITH
RIGID CORE 295 13.1.3 MOVING CORE 301 13.1.4 DROP VOLUME 305 13.2
OSCILLATIONS OF VISCOUS DROPS: THE LINEAR MODEL 307 13.2.1 MODEL 1 308
CONTENTS XVII 13.3 NONLINEAR THREE-DIMENSIONAL OSCILLATIONS OF
AXISYMMETRIC DROPS 322 13.3.1 NONLINEAR RESONANCES IN DROP OSCILLATION
330 13.4 OTHER NONLINEAR EFFECTS IN DROP OSCILLATIONS 340 13.5 SOLITONS
ON THE SURFACE OF LIQUID DROPS 344 13.6 PROBLEMS 353 14 OTHER SPECIAL
NONLINEAR COMPACT SYSTEMS 355 14.1 NONLINEAR COMPACT SHAPES AND
COLLECTIVE MOTION 355 14.2 THE HAMILTONIAN STRUCTURE FOR FREE BOUNDARY
PROBLEMS ON COMPACT SURFACES 359 PART III PHYSICAL NONLINEAR SYSTEMS AT
DIFFERENT SCALES 15 FILAMENTS, CHAINS, AND SOLITONS 367 15.1 VORTEX
FILAMENTS 367 15.1.1 GAS DYNAMICS FILAMENT MODEL AND SOLITONS 372 15.1.2
SPECIAL SOLUTIONS 375 15.1.3 INTEGRATION OF SERRET-FRENET EQUATIONS FOR
FILAMENTS . . 377 15.1.4 THE RICCATI FORM OF THE SERRET-FRENET EQUATIONS
380 15.1.5 SOLITON SOLUTIONS ON THE VORTEX FILAMENT 381 15.1.6 VORTEX
FILAMENTS AND THE NONLINEAR SCHROEDINGER EQUATION 384 15.2 NONLINEAR
DYNAMICS OF STIFF CHAINS 387 15.3 PROBLEMS 390 16 SOLITONS ON THE
BOUNDARIES OF MICROSCOPIC SYSTEMS 391 16.1 FIELD THEORY MODEL ON A
CLOSED CONTOUR AND INSTANTONS . 392 16.1.1 QUANTIZATION: EXCITED
STATES 394 16.1.2 QUANTIZATION: INSTANTONS AND TUNNELING 394 16.2
CLUSTERS AS SOLITARY WAVES ON THE NUCLEAR SURFACE 396 16.3 SOLITONS AND
QUASIMOLECULAR STRUCTURE 404 16.4 SOLITON MODEL FOR HEAVY EMITTED
NUCLEAR CLUSTERS 406 16.4.1 QUINTIC NONLINEAR SCHROEDINGER EQUATION FOR
NUCLEAR CLUSTER DECAY 408 16.5 CONTOUR SOLITONS IN THE QUANTUM HALL
LIQUID 411 16.5.1 PERTURBATIVE APPROACH 414 16.5.2 GEOMETRIE APPROACH
417 17 NONLINEAR CONTOUR DYNAMICS IN MACROSCOPIC SYSTEMS . 423 17.1
PLASMA VORTEX 423 17.1.1 EFFECTIVE SURFACE TENSION IN
MAGNETOHYDRODYNAMICS AND PLASMA SYSTEMS 423 17.1.2 TRAJECTORIES IN
MAGNETIC FIELD CONFIGURATIONS 424 17.1.3 MAGNETIC SURFACES IN STATIC
EQUILIBRIUM 433 XVIII CONTENTS 17.2 ELASTIC SPHERES 440 17.3 NONLINEAR
EVOLUTION OF OSCILLATION MODES IN NEUTRON STARS . . 441 18 MATHEMATICAL
ANNEX 445 18.1 DIFFERENTIABLE MANIFOLDS 445 18.2 RICCATI EQUATION 446
18.3 SPECIAL FUNCTIONS 446 18.4 ONE-SOLITON SOLUTIONS FOR THE KDV, MKDV,
AND THEIR COMBINATION 448 18.5 SCALING AND NONLINEAR DISPERSION
RELATIONS 450 REFERENCES 453 INDEX 461 |
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| classification_rvk | UF 5100 |
| classification_tum | PHY 013f |
| ctrlnum | (OCoLC)166358159 (DE-599)DNB984490221 |
| dewey-full | 531/.1133 530.14 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics 530 - Physics |
| dewey-raw | 531/.1133 530.14 |
| dewey-search | 531/.1133 530.14 |
| dewey-sort | 3531 41133 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV023222400 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:16:33Z |
| indexdate | 2024-07-09T21:13:26Z |
| institution | BVB |
| isbn | 9783540728726 3540728724 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016408267 |
| oclc_num | 166358159 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | XIX, 464 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer complexity Springer Series in synergetics |
| spelling | Ludu, Andrei Verfasser aut Nonlinear waves and solitons on contours and closed surfaces Andrei Ludu Berlin [u.a.] Springer 2007 XIX, 464 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer complexity Springer Series in synergetics Literaturverz. S. 453 - 460 Mathematik Compact spaces Nonlinear waves Mathematics Solitons Mathematics Soliton (DE-588)4135213-0 gnd rswk-swf Kompakter Raum (DE-588)4164857-2 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 s Soliton (DE-588)4135213-0 s Kompakter Raum (DE-588)4164857-2 s 1\p DE-604 DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016408267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ludu, Andrei Nonlinear waves and solitons on contours and closed surfaces Mathematik Compact spaces Nonlinear waves Mathematics Solitons Mathematics Soliton (DE-588)4135213-0 gnd Kompakter Raum (DE-588)4164857-2 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| subject_GND | (DE-588)4135213-0 (DE-588)4164857-2 (DE-588)4042102-8 |
| title | Nonlinear waves and solitons on contours and closed surfaces |
| title_auth | Nonlinear waves and solitons on contours and closed surfaces |
| title_exact_search | Nonlinear waves and solitons on contours and closed surfaces |
| title_exact_search_txtP | Nonlinear waves and solitons on contours and closed surfaces |
| title_full | Nonlinear waves and solitons on contours and closed surfaces Andrei Ludu |
| title_fullStr | Nonlinear waves and solitons on contours and closed surfaces Andrei Ludu |
| title_full_unstemmed | Nonlinear waves and solitons on contours and closed surfaces Andrei Ludu |
| title_short | Nonlinear waves and solitons on contours and closed surfaces |
| title_sort | nonlinear waves and solitons on contours and closed surfaces |
| topic | Mathematik Compact spaces Nonlinear waves Mathematics Solitons Mathematics Soliton (DE-588)4135213-0 gnd Kompakter Raum (DE-588)4164857-2 gnd Nichtlineare Welle (DE-588)4042102-8 gnd |
| topic_facet | Mathematik Compact spaces Nonlinear waves Mathematics Solitons Mathematics Soliton Kompakter Raum Nichtlineare Welle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016408267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT luduandrei nonlinearwavesandsolitonsoncontoursandclosedsurfaces |