Wigner measure and semiclassical limits of nonlinear Schrödinger equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Courant Inst. of Math. Sciences [u.a.]
2008
|
| Series: | Courant lecture notes in mathematics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 193-197) |
| Physical Description: | VIII, 197 S. |
| ISBN: | 9780821847015 0821847015 |
Staff View
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| 245 | 1 | 0 | |a Wigner measure and semiclassical limits of nonlinear Schrödinger equations |c Ping Zhang |
| 264 | 1 | |a New York |b Courant Inst. of Math. Sciences [u.a.] |c 2008 | |
| 300 | |a VIII, 197 S. | ||
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| 490 | 1 | |a Courant lecture notes in mathematics |v 17 | |
| 500 | |a Includes bibliographical references (p. 193-197) | ||
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Record in the Search Index
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| adam_text | Contents
Preface vii
Chapter 1. The Classical WKB Method 1
1.1. Introduction 1
1.2. WKB Approximation to the Linear Schrodinger Equation 2
1.3. The WKB Approximation to Nonlinear Schrodinger Equation 5
1.4. References and Remarks 10
Chapter 2. Wigner Measure 11
2.1. Semiclassical Pseudodifferential Operators and the FBI Transform 11
2.2. Wigner Measure 14
2.3. Semiclassical Limit of the Linear Schrodinger Equation 30
2.4. References and Remarks 34
Chapter 3. The Limit from the One-Dimensional Schrodinger-Poisson
to Vlasov-Poisson Equations 37
3.1. Introduction 37
3.2. Uniform Estimates 42
3.3. The Limit to the Vlasov-Poisson Equations 46
3.4. The Main Theorem 73
3.5. Mixed State Case 76
3.6. References and Remarks 79
Chapter 4. Semiclassical Limit of Schrodinger-Poisson Equations 81
4.1. Introduction 81
4.2. Preliminaries 84
4.3. Modulated Energy Estimate 89
4.4. The Main Theorem 95
4.5. References and Remarks 104
Chapter 5. Semiclassical Limit of the Cubic Schrodinger Equation
in an Exterior Domain 105
5.1. Introduction 105
5.2. Local Existence of a Smooth Solution to (5.7)-(5.8) 109
5.3. Uniform and Modulated Energy Estimates 115
5.4. Semiclassical Limit of the Cubic Schrodinger Equation 125
5.5. References and Remarks 127
V
vi CONTENTS
Chapter 6. Incompressible and Compressible Limits of Coupled Systems
of Nonlinear Schrodinger Equations 129
6.1. Introduction 129
6.2. Conservation Laws 131
6.3. Incompressible Limit of (6.1) 136
6.4. Compressible Limit of (6.2) 146
6.5. References and Remarks 152
Chapter 7. High-Frequency Limit of the Helmholtz Equation 153
7.1. Introduction . 153
7.2. Uniform Estimate for Solutions of (7.1) 154
7.3. Limit to the Liouville Equation 159
7.4. References and Remarks 171
Appendix A. Global Solutions to (3.14) 173
Appendix B. Denseness of Polynomials 177
Appendix C. Global Existence of a Solution to (5.1) 179
Appendix D. Global Smooth Solution to (6.1) 189
Bibliography 193
|
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| id | DE-604.BV025543137 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:36:11Z |
| institution | BVB |
| isbn | 9780821847015 0821847015 |
| language | English |
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| owner | DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-11 DE-91G DE-BY-TUM |
| physical | VIII, 197 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Courant Inst. of Math. Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Zhang, Ping 1957- Verfasser (DE-588)1012212335 aut Wigner measure and semiclassical limits of nonlinear Schrödinger equations Ping Zhang New York Courant Inst. of Math. Sciences [u.a.] 2008 VIII, 197 S. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 17 Includes bibliographical references (p. 193-197) Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Wigner-Verteilung (DE-588)4641021-1 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Wigner-Verteilung (DE-588)4641021-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3117-4 Courant lecture notes in mathematics 17 (DE-604)BV012714106 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020144551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Ping 1957- Wigner measure and semiclassical limits of nonlinear Schrödinger equations Courant lecture notes in mathematics Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Wigner-Verteilung (DE-588)4641021-1 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4641021-1 |
| title | Wigner measure and semiclassical limits of nonlinear Schrödinger equations |
| title_auth | Wigner measure and semiclassical limits of nonlinear Schrödinger equations |
| title_exact_search | Wigner measure and semiclassical limits of nonlinear Schrödinger equations |
| title_full | Wigner measure and semiclassical limits of nonlinear Schrödinger equations Ping Zhang |
| title_fullStr | Wigner measure and semiclassical limits of nonlinear Schrödinger equations Ping Zhang |
| title_full_unstemmed | Wigner measure and semiclassical limits of nonlinear Schrödinger equations Ping Zhang |
| title_short | Wigner measure and semiclassical limits of nonlinear Schrödinger equations |
| title_sort | wigner measure and semiclassical limits of nonlinear schrodinger equations |
| topic | Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Wigner-Verteilung (DE-588)4641021-1 gnd |
| topic_facet | Nichtlineare Schrödinger-Gleichung Wigner-Verteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020144551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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