Mathematical structures in continuous dynamical systems: Poisson systems and complete integrability with applications from fluid dynamics
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1994
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| Series: | Studies in mathematical physics
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 617 S. graph. Darst. |
| ISBN: | 0444821511 |
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| 245 | 1 | 0 | |a Mathematical structures in continuous dynamical systems |b Poisson systems and complete integrability with applications from fluid dynamics |c E. van Groesen ; E. M. de Jager |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1994 | |
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| adam_text | IMAGE 1
MATHEMATICAL S T R U C T U R ES
IN C O N T I N U O US DYNAMICAL SYSTEMS
POISSON SYSTEMS A ND COMPLETE INTEGRABILITY WITH APPLICATIONS FROM FLUID
DYNAMICS
E. VAN GROESEN DEPT. OF APPLIED MATHEMATICS UNIVERSITY OFTWENTE
ENSCHEDE, THE NETHERLANDS
E.M. DE J A G E R, E M E R I T US
DEPT. OF MATHEMATICS AND COMPUTER SCIENCE UNIVERSITY OF AMSTERDAM
AMSTERDAM, THE NETHERLANDS
NORTH-HOLLAND
IMAGE 2
CONTENTS
PREFACE V
CONTENTS VII
PART I - POISSON STRUCTURES IN FLUID DYNAMICS INTRODUCTION TO PART I 3
1. POISSON STRUCTURES 9
INTRODUCTION 9
1.1. GENERAL DEFINITIONS AND OUTLINE 12
1.2. FINITE DIMENSIONAL SYSTEMS 18
TANGENT AND COTANGENT SPACE, VECTOR FIELDS 18
HAMILTONIAN VECTOR FIELDS AND STRUCTURE MAP 20
POISSON DYNAMICS 21
SYMPLECTIC STRUCTURE AND HAMILTONIAN SYSTEMS 21
1.3. EXAMPLES 22
CANONICAL HAMILTONIAN SYSTEMS 22
LAGRANGIAN SYSTEMS 24
PARTICLE MOTION IN PLANE FLUID FLOWS 26
KIRCHHOFES EQUATIONS FOR VORTEX POINTS 26
COMPLEX CANONICAL STRUCTURE 28
DEGENERATE HAMILTONIAN SYSTEMS 28
DARBOUX THEOREM 29
RIGID BODY ROTATIONS 30
MAGNETIC SPIN SYSTEMS 34
1.4. SUMMARY OF VARIATIONAL CALCULUS 35
FIRST VARIATION AND VARIATIONAL DERIVATIVE 35
STATIONARITY CONDITION 38
VII
IMAGE 3
EULER-LAGRANGE EQUATION FOR UNCONSTRAINED PROBLEMS . 39
VARIATIONAL PRINCIPLES IN MATHEMATICAL PHYSICS 40
SECOND VARIATION FOR UNCONSTRAINED PROBLEMS 42
CONSTRAINED PROBLEMS AND LAGRANGE S MULTIPLIER RULE . 44 CONSTRAINED
SECOND VARIATION 45
1.5. INFINITE DIMENSIONAL POISSON SYSTEMS 47
POISSON BRACKET AND STATE EQUATION 47
CANONICAL CONTINUUM DESCRIPTION 48
LAGRANGIAN SYSTEMS 50
STRUCTURE MAPS 50
SYMPLECTIC STRUCTURES 52
1.6. EXAMPLES FROM MATHEMATICAL PHYSICS 53
MAXWELL S EQUATIONS 54
SINE-GORDON EQUATION 55
SCHROEDINGER S EQUATION 56
NONLINEAR SCHROEDINGER EQUATION 57
1.7. WAVE EQUATIONS 57
UNI-DIRECTIONAL WAVE EQUATIONS 59
BI-DIRECTIONAL WAVE EQUATIONS 63
REFERENCES 66
2. SURFACE WAVES 69
INTRODUCTION 69
2.1. HAMILTONIAN STRUCTURE OF THE BASIC EQUATIONS 70
BASIC EQUATIONS 70
HAMILTONIAN FORMULATION 72
TRANSFORMATION OF BASIC VARIABLES 74
2.2. APPROXIMATIONS FOR THE KINETIC ENERGY 75
LINEAR THEORY: INFINITESIMAL SURFACE WAVES 76
TIDAL WAVE APPROXIMATION 78
BOUSSINESQ APPROXIMATION 79
2.3. UNI-DIRECTIONALIZATION TO KDV-EQUATION 80
TRANSFORMATION TO UNI-DIRECTIONAL VARIABLES 81
UNI-DIRECTIONALIZATION 82
2.4. MODIFICATIONS FOR VARYING BOTTOM 86
DERIVATION OF BI-DIRECTIONAL EQUATION 87
TRANSFORMATION TO UNI-DIRECTIONAL VARIABLES 89
UNI-DIRECTIONAL INFINITESIMAL WAVES WITHOUT DISPERSION . 90 GENERALIZED
KDV-EQUATION 97
REFERENCES 100
3. EULEHAN FLUID DYNAMICS 103
INTRODUCTION 103
3.1. TRANSFORMATION TO EULERIAN DESCRIPTION 107
COMPRESSIBLE ISENTROPIC FLOWS 107
NON-ISENTROPIC FLOWS 112
INCOMPRESSIBLE FLOWS 114
VORTICITY FORMULATION 117
VIII
IMAGE 4
3.2. INCOMPRESSIBLE PLANE FLOWS 118
VELOCITY FORMULATION 119
VORTICITY FORMULATION 119
ENSTROPHY CASIMIR FUNCTIONALS 120
CONSISTENT DERIVATION OF KIRCHHOFF S EQUATIONS 121
3.3. INCOMPRESSIBLE AXIALLY SYMMETRIE FLOWS 122
CASIMIR FUNCTIONALS 124
REFERENCES 125
4. CONSISTENT MODELLING 127
INTRODUCTION 127
4.1. TRANSFORMATIONS 132
TRANSFORMATION OF THE BRACKET 133
TRANSFORMATION OF THE STATE EQUATION 135
POISSON MAPS 139
HAMILTONIAN FLOWS ARE POISSON MAPS 140
CANONICAL TRANSFORMATIONS 141
4.2. REDUCTION 142
DECOMPOSITION 142
POISSON SUBMANIFOLD 144
REDUCED MANIFOLDS 145
4.3. RESTRICTED DYNAMICS ON A GIVEN MANIFOLD 147
MANIFOLDS OF PARAMETERIZED FUNETIONS 147
RESTRICTED DYNAMICS 148
PROJECTED DYNAMICS 149
TRUNCATED DYNAMICS 149
REPARAMETRIZATION OF THE MANIFOLD 152
4.4. THE RESTRICTED DYNAMICS COUPLED WITH THE REMAINDER 153
DECOMPOSITION BASED ON A SUBMANIFOLD 153
DECOMPOSITION OF THE EVOLUTION EQUATION 155
DECOMPOSITION OF THE POISSON STRUETURE 156
RESTRICTING THE DYNAMICS TO THE MANIFOLD 157
DIRAC DYNAMICS 158
RESTRICTION OF FIRST INTEGRALS 160
4.5. UNBALANCED DIAGONAL STRUETURE MAPS 161
DIAGONAL STRUETURE MAPS 161
REGULAER PERTURBATION PROBLEMS 162
SINGULAR PERTURBATION PROBLEMS 163
4.6. LARGE AND SMALL SCALE INTERACTIONS 166
DIRECT FOURIER SEPARATION 166
TRUNCATIONS FOR 1D WAVE EQUATIONS 168
UNBALANCED CONTRIBUTION FROM THE SMALL AND LARGE SCALES 169 REGULAER
PERTURBATION OF THE TRUNCATED BBM-EQUATION . 171 SINGULAR PERTURBATION
OF THE TRUNCATED KDV-EQUATION . 171 REFERENCES 173
5. POISSON DYNAMICS 175
INTRODUCTION 175
IX
IMAGE 5
5.1. HAMILTONIAN SYSTEMS WITH A CYCLIC VARIABLE 183
EQUILIBRIUM SOLUTIONS 184
REDUCED DYNAMICS 184
EQUILIBRIA OF THE REDUCED DYNAMICS 185
RELATIEVE EQUILIBRIA 185
RELATIVE EQUILIBRIUM SOLUTIONS 187
STABILITY 188
5.2. RELATIVE EQUILIBRIA 190
FIRST INTEGRALS AND CASIMIR FUNCTIONALS 191
CONSTRAINED HAMILTONIAN EXTREMIZERS 192
BRANCHES OF CONSTRAINED EXTREMIZERS AND VALUE FUNCTION 195 MANIFOLD OF
RELATIVE EQUILIBRIA 197
RELATIVE EQUILIBRIUM SOLUTIONS 198
RELATIVE EQUILIBRIA WITH MORE INTEGRALS 200
DYNAMICAL INVARIANCE OF THE CRITICAL POINT SET OF INTEGRALS 203 5.3.
SYMMETRIES AND COMMUTING FLOWS 204
SYMMETRIES OF EVOLUTION EQUATIONS 205
COMMUTING FLOWS 205
THE LIE-BRACKET OF HAMILTONIAN VECTOR FIELDS 208
5.4. REDUCTION PROCEDURE 210
REDUCTION WITH ONE INTEGRAL 211
REDUCTION WITH MORE INTEGRALS IN INVOLUTION 214
COMPLETE INTEGRABILITY 216
5.5. STABILITY 217
LYAPUNOV STABILITY OF EQUILIBRIA AND INVARIANT SETS . . . 217
LYAPUNOV FUNCTIONALS 219
GEOMETRIE SQUEEZING PROPERTY OF C 220
STABILITY OF A NON-DEGENERATE MINIMIZER 222
STABILITY OF INVARIANT SETS 223
ENERGETICS FOR POISSON SYSTEMS 225
CONSTRAINED STABILITY 227
UNCONSTRAINED STABILITY 229
REFERENCES 231
6. COHERENT STRUCTURES AS RELATIVE EQUILIBRIA 233
INTRODUCTION 233
6.1. VORTEX POINTS 236
MOMENTUM INTEGRALS AND THEIR FLOWS 237
RELATIVE EQUILIBRIA 238
TWO POINT VORTICES 239
THREE POINT VORTICES 242
6.2. TRAVELLING WAVES 244
KDV-TYPE OF EQUATIONS 245
KDV-SOLITONS 248
KDV-CNOIDAL WAVES 248
KDV - SOLITARY WAVE INTERACTION 249
BBM-EQUATION 253
OPTICAL SOLITONS 254
X
IMAGE 6
6.3. VORTICES IN PLANE BOUNDED DOMAINS 255
CASIMIR FUNCTIONALS 257
BASIC VARIATIONAL FORMULATIONS 257
INTERMEZZO: CONVEXITY METHODS 258
DUAL FORMULATION 260
CONFINEMENT AND NON-DIFFERENTIABILITY 260
PATCHES 261
CONFINED MONOPOLE VORTICES UNFOLDED FROM TAYLOR VORTICES 263
DIPOLAR VORTICES 266
6.4. CONFINED VORTICES IN THE PLANE 267
RENORMALIZATION OF FUNCTIONALS 269
INTEGRALS AND THEIR FLOWS 271
BASIC VARIATIONAL FORMULATION 272
CIRCULAR PATCHES 274
LEITH VORTICES 278
CLOCKWISE ROTATING, MAXIMUM ENERGY MONOPOLES . . .. 279
COUNTER-CLOCKWISE ROTATING, MINIMUM ENERGY MONOPOLES 281 6.5. SWIRLING
PIPE FLOWS 283
CROSS-SECTIONAL ENERGY AND HELICITY INTEGRALS 285
THE BASIC VARIATIONAL PRINCIPLE 286
SWIRLING FLOWS AS RELATIVE EQUILIBRIA 287
BRAGG-HAWTHORNE EQUATION 289
REFERENCES 290
7. POISSON PERTURBATION METHODS 293
INTRODUCTION 293
7.1. DISSIPATIVE POISSON SYSTEMS 300
DISSIPATIVE STRUCTURES 301
DISSIPATIVE POISSON STRUCTURES 304
RAYLEIGH DISSIPATION FUNCTIONAL 306
7.2. THERMODYNAMIC SYSTEMS 307
CONSTRAINED DISSIPATIVE SYSTEMS 307
THERMODYNAMIC SYSTEMS 309
7.3. APPROXIMATIONS WITH RELATIVE EQUILIBRIA 311
QUALITY OF APPROXIMATIONS MEASURED BY FUNCTIONALS . . 311 APPROXIMATIONS
USING RELATIVE EQUILIBRIA 313
EQUATION FOR THE ERROR 315
7.4. DECAYING AND SELF-EXCITING SURFACE WAVES 319
DISSIPATIVE LINEAR WAVE EQUATIONS 319
DISSIPATING KDV-CNOIDAL WAVES, NUMERICS 323
DISSIPATING KDV-CNOIDAL WAVES, THEORY 326
SELF-EXCITED KDV-CNOIDAL WAVES 329
7.5. SELF-ORGANIZATION IN PLANE VISCOUS FLUIDS 332
FORMULATION OF THE PLANE FLOW PROBLEM 333
PLANAR TAYLOR VORTICES 333
SELF-ORGANIZATION PROCESS 335
FLOW OF AVERAGED SPECTRAL ENERGY AND ENSTROPHY 338
XI
IMAGE 7
7.6. VISCOUS DECAY OF MONOPOLES ON THE PLANE 340
VISCOUS DECAY OF INTEGRALS 341
DECAY OF CIRCULAR PATCHES 342
INCONSISTENT EVOLUTION ALONG LEITH VORTICES 343
VISCOUS INSTABILITY OF MAXIMUM ENERGY MONOPOLES . . . 345 VISCOUS
STABILITY OF MINIMUM ENERGY MONOPOLES 347
SUMMARY 350
REFERENCES 350
PART II - MATHEMATICAL INTRODUCTION TO THE THEORY OF SOLITONS
INTRODUCTION TO PART II 355
1. SOLITONS IN PHYSICS AND MATHEMATICS 359
1.1. HISTORY 359
1.2. THE FERMI, PASTA, ULAM EXPERIMENTS 362
1.3. PERIODIC SOLUTIONS OF THE PERIODIC TODA CHAIN 365
1.4. SOLITARY WAVE SOLUTIONS OF THE INFINITE TODA CHAIN 370
1.5. FINITE TODA CHAIN AS INTEGRABLE HAMILTON-POISSON SYSTEM 375
1.5.1. INTRODUCTION 375
1.5.2. A POISSON-HAMILTON STRUCTURE ON A MATRIX LIE ALGEBRA . . . 377
1.5.3. DECOMPOSITION OF MATRIX LIE ALGEBRAS AND RESTRICTED DYNAMICAL
SYSTEMS 380
1.5.4. APPLICATION TO THE FINITE TODA CHAIN 384
1.6. THE FINITE TODA CHAIN IN THE LAX FORMALISM 386
1.7. THE INFINITE TODA CHAIN IN THE LAX FORMALISM 388
1.8. THE KDV-EQUATION FOR LONG WAVES IN A CANAL 391
1.8.1. THE DERIVATION BY KORTEWEG AND DE VRIES 392
1.8.2. THE DERIVATION OF THE KORTEWEG-DE VRIES EQUATION USING MULTIPLE
SCALES 395
1.9. KDV AS A CONTINUUM APPROXIMATION OF A DISCRETE SYSTEM 402
1.10. THE THEORY OF P. LAX 403
1.11. AN ALGEBRAIC APPROACH BY CHERN AND PENG 408
1.12. WAVE SOLUTIONS OF THE KDV-EQUATION 412
2. A.K.N.S. SYSTEMS AND SOLITON EQUATIONS 419
2.1. AN EIGENVALUE PROBLEM 419
2.2. THE FAMILY OF THE KORTEWEG-DE VRIES EQUATIONS 422
2.3. OTHER FAMILIES OF SOLITON EQUATIONS 427
2.4. THE SINE-GORDON EQUATION 430
2.5. A.K.N.S. SYSTEMS AND LAX PAIRS 433
2.6. NLS, A PHYSICAL MODEL AND A SOLITON SOLUTION 437
2.7. WAVE SOLUTIONS OF THE SINE-GORDON EQUATION 444
3. SCATTERING, INVERSE SCATTERING AND SOLITONS 449
3.1. INTRODUCTION 449
3.2. DIRECT SCATTERING 452
XII
IMAGE 8
3.3. INVERSE SCATTERING 468
3.4. THE TIME EVOLUTION OF THE SCATTERING DATA 473
3.5. INITIAL VALUE PROBLEMS AND SOLITONS 477
3.6. THE METHOD OF BILINEARIZATION 487
3.6.1. THE BILINEARIZATION 487
3.6.2. THE IV-SOLITON SOLUTION FOR THE KDV-EQUATION AND A GENERALIZATION
489
3.6.3. A FURTHER GENERALIZATION 494
3.6.4. THE T-FUNCTION AS UNIVERSAL SOLUTION OF THE KDV-HIERARCHY . 494
4. BAECKLUND-TRANSFORMATIONS 497
4.1. INTRODUCTION 498
4.2. BAECKLUND TRANSFORMATION FOR SINE-GORDON EQUATION 500
4.3. NONLINEAR SUPERPOSITION PRINCIPLE FOR SINE-GORDON 502
4.3.1. THE STATIONARY KINK SOLUTION 502
4.3.2. THE NONLINEAR SUPERPOSITION PRINCIPLE AND THE TWO-KINK SOLUTION
503
4.4. THE BAECKLUND TRANSFORMATION FOR KDV 508
4.5. NONLINEAR SUPERPOSITION PRINCIPLE FOR KDV 513
4.6. BAECKLUND TRANSFORMATIONS AND INVERSE SCATTERING 516
4.6.1. THE ADDITION THEOREM OF DEIFT AND TRUBOWITZ 516
4.6.2. PROOF OF THE ADDITION THEOREM 518
4.6.3. SUMMARY AND CONSEQUENCES 523
4.6.4. BAECKLUND TRANSFORMATIONS BY INVERSE SCATTERING 524
4.7. THE T-FUNCTION AND ITS BAECKLUND TRANSFORMATION 535
4.7.1. INTRODUCTION 535
4.7.2. APPLICATION 538
5. THE KDV-HIERARCHY AS A HIERARCHY OF HAMILTONIAN SYSTEMS . 543 5.1.
HAMILTONIAN SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 544
5.2. HAMILTONIAN SYSTEMS OF EVOLUTION EQUATIONS 546
5.3. HAMILTONIAN REPRESENTATION OF THE KDV-EQUATIONS 552
5.3.1. CONSERVED FUNCTIONALS 553
5.3.2. THE HAMITONIAN STRUCTURE OF THE KDV-FAMILY 556
5.4. BI-HAMILTONIAN STRUCTURES AND INTEGRABILITY OF KDV-EQUATIONS . . .
560
6. PROLONGATION STRUCTURES 565
6.1. CARTAN PROLONGATIONS 566
6.2. A PROLONGATION OF THE KDV-EQUATION 571
6.3. THE GENERAL PROLONGATION OF THE KDV-EQUATION 579
6.4. A PROLONGATION OF THE SINE-GORDON-EQUATION 583
6.5. A PROLONGATION OF THE NONLINEAR SCHROEDINGER-EQUATION 587
6.5.1. THE TWO-DIMENSIONAL LINEAR PROLONGATION . . 587
6.5.2. THE ISOSPECTRAL PARAMETER A 593
XIII
IMAGE 9
SUBJECT INDEX SSG?
REFERENCES SSQ3
|
| any_adam_object | 1 |
| author | Groesen, Embrecht W. van Jager, Eduardus M. de |
| author_facet | Groesen, Embrecht W. van Jager, Eduardus M. de |
| author_role | aut aut |
| author_sort | Groesen, Embrecht W. van |
| author_variant | e w v g ewv ewvg e m d j emd emdj |
| building | Verbundindex |
| bvnumber | BV010477279 |
| classification_rvk | SK 520 SK 950 |
| classification_tum | PHY 220f PHY 013f |
| ctrlnum | (OCoLC)231651724 (DE-599)BVBBV010477279 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010477279 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:53:09Z |
| institution | BVB |
| isbn | 0444821511 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006981034 |
| oclc_num | 231651724 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-703 DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-384 DE-12 DE-703 DE-91G DE-BY-TUM DE-11 |
| physical | XIV, 617 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | North-Holland |
| record_format | marc |
| series | Studies in mathematical physics |
| series2 | Studies in mathematical physics |
| spelling | Groesen, Embrecht W. van Verfasser aut Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics E. van Groesen ; E. M. de Jager Amsterdam North-Holland 1994 XIV, 617 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in mathematical physics 6 Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Poisson-Gleichung (DE-588)4174972-8 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Poisson-Gleichung (DE-588)4174972-8 s Hydrodynamik (DE-588)4026302-2 s DE-604 Soliton (DE-588)4135213-0 s Strömungsmechanik (DE-588)4077970-1 s Jager, Eduardus M. de Verfasser aut Studies in mathematical physics 6 (DE-604)BV004808178 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006981034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Groesen, Embrecht W. van Jager, Eduardus M. de Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics Studies in mathematical physics Hydrodynamik (DE-588)4026302-2 gnd Soliton (DE-588)4135213-0 gnd Poisson-Gleichung (DE-588)4174972-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4135213-0 (DE-588)4174972-8 (DE-588)4077970-1 |
| title | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics |
| title_auth | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics |
| title_exact_search | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics |
| title_full | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics E. van Groesen ; E. M. de Jager |
| title_fullStr | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics E. van Groesen ; E. M. de Jager |
| title_full_unstemmed | Mathematical structures in continuous dynamical systems Poisson systems and complete integrability with applications from fluid dynamics E. van Groesen ; E. M. de Jager |
| title_short | Mathematical structures in continuous dynamical systems |
| title_sort | mathematical structures in continuous dynamical systems poisson systems and complete integrability with applications from fluid dynamics |
| title_sub | Poisson systems and complete integrability with applications from fluid dynamics |
| topic | Hydrodynamik (DE-588)4026302-2 gnd Soliton (DE-588)4135213-0 gnd Poisson-Gleichung (DE-588)4174972-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Hydrodynamik Soliton Poisson-Gleichung Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006981034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004808178 |
| work_keys_str_mv | AT groesenembrechtwvan mathematicalstructuresincontinuousdynamicalsystemspoissonsystemsandcompleteintegrabilitywithapplicationsfromfluiddynamics AT jagereduardusmde mathematicalstructuresincontinuousdynamicalsystemspoissonsystemsandcompleteintegrabilitywithapplicationsfromfluiddynamics |