Solutions of nonlinear Schrödinger systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2015
|
| Series: | Springer theses
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XI, 180 S. |
| ISBN: | 3662454777 9783662454770 |
Staff View
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Record in the Search Index
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CONTENTS
1 INTRODUCTION 1
1.1 MATHEMATICAL MODEL ARISING FROM PHYSICS 1
1.2 OVERVIEW OF PREVIOUS RESEARCH 3
1.2.1 GROUND STATE SOLUTIONS 3
1.2.2 MULTIPLE SOLUTIONS 5
1.3 PROBLEMS STUDIED IN THIS THESIS 6
2 A BEC SYSTEM WITH DIMENSIONS N =
2,3: GROUND STATE
SOLUTIONS 9
2.1 MAIN RESULTS 9
2.2 UNIQUENESS OF POSITIVE SOLUTIONS 14
2.3 OPTIMAL PARAMETER RANGE 18
3 A BEC SYSTEM WITH DIMENSIONS N = 2,3I SIGN-CHANGING
SOLUTIONS 29
3.1 MAIN RESULTS 29
3.2 SIGN-CHANGING SOLUTIONS 32
3.3 SEMI-NODAL SOLUTIONS 50
4 A BEC SYSTEM WITH DIMENSIONS N = 4: CRITICAL CASE 57
4.1 MAIN RESULTS 57
4.2 THE SIMPLE CASE X| = X2 63
4.3 THE LIMIT PROBLEM 64
4.4 UNIQUENESS OF GROUND STATE SOLUTIONS 67
4.5 THE GENERAL CASE A.I ^ A.2 70
4.6 PHASE SEPARATION 86
5 A GENERALIZED BEC SYSTEM WITH CRITICAL EXPONENTS
IN DIMENSIONS N 5 97
5.1 MAIN RESULTS 97
5.2 THE SYMMETRIC CASE XI = X2 104
IX
HTTP://D-NB.INFO/1059095610
X CONTENTS
5.3 THE GENERAL CASE K] ^ X.2 121
5.4 UNIQUENESS OF GROUND STATE SOLUTIONS 138
5.5 PHASE SEPARATION AND SIGN-CHANGING SOLUTIONS
OF BREZIS-NIRENBERG PROBLEM 142
5.6 SHARP ENERGY ESTIMATES FOR BREZIS-NIRENBERG PROBLEM 148
6 A LINEARLY COUPLED SCHRDDINGER SYSTEM WITH CRITICAL
EXPONENT 157
6.1 MAIN RESULTS 157
6.2 SHARP PARAMETER RANGES 162
6.3 ASYMPTOTICS 172
REFERENCES 175
INDEX 179 |
| any_adam_object | 1 |
| author | Chen, Zhijie |
| author_GND | (DE-588)1072723980 |
| author_facet | Chen, Zhijie |
| author_role | aut |
| author_sort | Chen, Zhijie |
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| bvnumber | BV042610878 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)893438759 (DE-599)DNB1059095610 |
| discipline | Mathematik |
| format | Thesis Book |
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| institution | BVB |
| isbn | 3662454777 9783662454770 |
| language | English |
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| spelling | Chen, Zhijie Verfasser (DE-588)1072723980 aut Solutions of nonlinear Schrödinger systems Zhijie Chen Berlin [u.a.] Springer 2015 XI, 180 S. txt rdacontent n rdamedia nc rdacarrier Springer theses Zugl.: Beijing, Tsinghua Univ., Diss., 2014 Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Bose-Einstein-Kondensation (DE-588)4402897-0 gnd rswk-swf Lösung Mathematik (DE-588)4120678-2 gnd rswk-swf Elliptisches System (DE-588)4121184-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Elliptisches System (DE-588)4121184-4 s Lösung Mathematik (DE-588)4120678-2 s Bose-Einstein-Kondensation (DE-588)4402897-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-662-45478-7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4789587&prov=M&dok_var=1&dok_ext=htm Inhaltstext DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/798564776.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028043770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Zhijie Solutions of nonlinear Schrödinger systems Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd Lösung Mathematik (DE-588)4120678-2 gnd Elliptisches System (DE-588)4121184-4 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4402897-0 (DE-588)4120678-2 (DE-588)4121184-4 (DE-588)4113937-9 |
| title | Solutions of nonlinear Schrödinger systems |
| title_auth | Solutions of nonlinear Schrödinger systems |
| title_exact_search | Solutions of nonlinear Schrödinger systems |
| title_full | Solutions of nonlinear Schrödinger systems Zhijie Chen |
| title_fullStr | Solutions of nonlinear Schrödinger systems Zhijie Chen |
| title_full_unstemmed | Solutions of nonlinear Schrödinger systems Zhijie Chen |
| title_short | Solutions of nonlinear Schrödinger systems |
| title_sort | solutions of nonlinear schrodinger systems |
| topic | Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd Lösung Mathematik (DE-588)4120678-2 gnd Elliptisches System (DE-588)4121184-4 gnd |
| topic_facet | Nichtlineare Schrödinger-Gleichung Bose-Einstein-Kondensation Lösung Mathematik Elliptisches System Hochschulschrift |
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| work_keys_str_mv | AT chenzhijie solutionsofnonlinearschrodingersystems |