The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory
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| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Brookline, Mass.
Math Sci Press
1977
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| Schriftenreihe: | Lie groups
7 |
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| 111 | 2 | |a Conference on Geometric Control Theory |d 1976 |c Moffett Field, Calif. |j Verfasser |0 (DE-588)817902-5 |4 aut | |
| 245 | 1 | 0 | |a The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |c ed. by Clyde Martin. Articles by J. Baillieul ... |
| 246 | 1 | 3 | |a The nineteen hundred and seventy-six Ames Research Center, NASA, Conference on Geometric Control Theory |
| 264 | 1 | |a Brookline, Mass. |b Math Sci Press |c 1977 | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
Page
PREFACE iii
DIFFERENTIAL GEOMETRIC PROLONGATIONS AND BACKLUND
TRANSFORMATIONS. Frank Estabrook, Hugo Wahlquist
and Robert Hermann 1
1. Introduction 1
2. The Basic Algebraic and Differential
Operations 5
3. The Natural Operations in Differential
Forms 7
4. Behavior of Differential Forms under
Mappings and Changes of Variables.
Integration. Stoke s Formula. Conserved
Currents 15
5. Exterior Differential Systems 21
6. Conservation Laws of Differential Equations
and Exterior Differential Systems 30
7. Conservation Laws and Prolongations 33
8. Multiple Pseudopotentials and Cartan
Ehresmann Connections 37
9. Multiple Prolongations Defined by Cartan
Ehresmann Connections with a Structure
Group 41
10. Linear Pseudopotentials and the Inverse
Scattering Equations 43
11. The Inverse Scattering Formalism as a
Complete Integrability Condition, Leading
to the Lax Equations. A Speculation about
the Inverse Scattering Equation in Higher
Dimensions 45
12. Specialization to the Korteweg de Vries
Schrodinger Operator 48
13. The Backlund Transformations Described in
Terms of Prolongations 54
Bibliography 62
Recent Literature of New Methods of
Differential Geometry Applied to Nonlinear
Partial Differential Equations and Soliton
Theory 64
vii
viii TABLE OF CONTENTS
Page
USING PSEUDOPOTENTIALS. James Corones 67
1. Introduction 67
2. A Brief Review of Pseudopotentials 69
3. An Example 77
4. Space Time Dependent Pseudopotentials 83
Bibliography 87
DIFFERENTIAL GEOMETRIC VIEWPOINTS ON THE DEVELOPMENT
OF SHOCK WAVES. Robert B. Gardner 89
Bibliography 104
BACKLUND TRANSFORMATIONS AND THE SINE GORDON EQUATION.
Hedley C. Morris 105
1. Prolongations 105
2. Backlund Transformations 109
3. Topological Charge [11] 113
4. The Massive Thirring Model 118
Bibliography 123
PROLONGATION STRUCTURES OF NONLINEAR EVOLUTION
EQUATIONS IN TWO AND THREE SPATIAL DIMENSIONS.
Hedley C. Morris 125
1. Generalizing a Known Case 126
2. An Extended Ideal 129
3. The Kadomtsev Petviashvili Dryuma
Equation 131
4. A Generalized Nonlinear Schrbdinger
Equation 135
5. Three Dimensions 143
Bibliography 146
A PLAUSIBILITY ARGUMENT FOR THE MARCHENKO EQUATION
Alwyn C. Scott 147
Bibliography 153
|
| adam_txt |
TABLE OF CONTENTS
Page
PREFACE iii
DIFFERENTIAL GEOMETRIC PROLONGATIONS AND BACKLUND
TRANSFORMATIONS. Frank Estabrook, Hugo Wahlquist
and Robert Hermann 1
1. Introduction 1
2. The Basic Algebraic and Differential
Operations 5
3. The Natural Operations in Differential
Forms 7
4. Behavior of Differential Forms under
Mappings and Changes of Variables.
Integration. Stoke's Formula. Conserved
Currents 15
5. Exterior Differential Systems 21
6. Conservation Laws of Differential Equations
and Exterior Differential Systems 30
7. Conservation Laws and Prolongations 33
8. Multiple Pseudopotentials and Cartan
Ehresmann Connections 37
9. Multiple Prolongations Defined by Cartan
Ehresmann Connections with a Structure
Group 41
10. Linear Pseudopotentials and the Inverse
Scattering Equations 43
11. The "Inverse Scattering" Formalism as a
"Complete Integrability" Condition, Leading
to the Lax Equations. A Speculation about
the Inverse Scattering Equation in Higher
Dimensions 45
12. Specialization to the Korteweg de Vries
Schrodinger Operator 48
13. The Backlund Transformations Described in
Terms of Prolongations 54
Bibliography 62
Recent Literature of New Methods of
Differential Geometry Applied to Nonlinear
Partial Differential Equations and Soliton
Theory 64
vii
viii TABLE OF CONTENTS
Page
USING PSEUDOPOTENTIALS. James Corones 67
1. Introduction 67
2. A Brief Review of Pseudopotentials 69
3. An Example 77
4. Space Time Dependent Pseudopotentials 83
Bibliography 87
DIFFERENTIAL GEOMETRIC VIEWPOINTS ON THE DEVELOPMENT
OF SHOCK WAVES. Robert B. Gardner 89
Bibliography 104
BACKLUND TRANSFORMATIONS AND THE SINE GORDON EQUATION.
Hedley C. Morris 105
1. Prolongations 105
2. Backlund Transformations 109
3. Topological Charge [11] 113
4. The Massive Thirring Model 118
Bibliography 123
PROLONGATION STRUCTURES OF NONLINEAR EVOLUTION
EQUATIONS IN TWO AND THREE SPATIAL DIMENSIONS.
Hedley C. Morris 125
1. Generalizing a Known Case 126
2. An Extended Ideal 129
3. The Kadomtsev Petviashvili Dryuma
Equation 131
4. A Generalized Nonlinear Schrbdinger
Equation 135
5. Three Dimensions 143
Bibliography 146
A PLAUSIBILITY ARGUMENT FOR THE MARCHENKO EQUATION
Alwyn C. Scott 147
Bibliography 153 |
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| index_date | 2024-07-02T16:19:06Z |
| indexdate | 2024-07-09T20:51:36Z |
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| language | English |
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| physical | 555 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Math Sci Press |
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| series | Lie groups |
| series2 | Lie groups |
| spelling | Conference on Geometric Control Theory 1976 Moffett Field, Calif. Verfasser (DE-588)817902-5 aut The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory ed. by Clyde Martin. Articles by J. Baillieul ... The nineteen hundred and seventy-six Ames Research Center, NASA, Conference on Geometric Control Theory Brookline, Mass. Math Sci Press 1977 555 S. txt rdacontent n rdamedia nc rdacarrier Lie groups 7 Théorie du contrôle fourier Geometrie (DE-588)4020236-7 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Geometrie (DE-588)4020236-7 s DE-604 Systemtheorie (DE-588)4058812-9 s Optimale Kontrolle (DE-588)4121428-6 s Martin, Clyde Sonstige oth Baillieul, John Sonstige oth Lie groups 7 (DE-604)BV000001596 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015376459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory Lie groups Théorie du contrôle fourier Geometrie (DE-588)4020236-7 gnd Systemtheorie (DE-588)4058812-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4058812-9 (DE-588)4121428-6 (DE-588)1071861417 |
| title | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_alt | The nineteen hundred and seventy-six Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_auth | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_exact_search | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_exact_search_txtP | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_full | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory ed. by Clyde Martin. Articles by J. Baillieul ... |
| title_fullStr | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory ed. by Clyde Martin. Articles by J. Baillieul ... |
| title_full_unstemmed | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory ed. by Clyde Martin. Articles by J. Baillieul ... |
| title_short | The 1976 Ames Research Center, NASA, Conference on Geometric Control Theory |
| title_sort | the 1976 ames research center nasa conference on geometric control theory |
| topic | Théorie du contrôle fourier Geometrie (DE-588)4020236-7 gnd Systemtheorie (DE-588)4058812-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Théorie du contrôle Geometrie Systemtheorie Optimale Kontrolle Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015376459&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001596 |
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