Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1997
|
| Series: | Applied mathematical sciences
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 161 - 167 |
| Physical Description: | VIII, 170 S. graph. Darst. |
| ISBN: | 0387949259 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011726669 | ||
| 003 | DE-604 | ||
| 005 | 20220422 | ||
| 007 | t | ||
| 008 | 980113s1997 gw d||| |||| 00||| ger d | ||
| 016 | 7 | |a 952457016 |2 DE-101 | |
| 020 | |a 0387949259 |c Pp. : DM 98.00 |9 0-387-94925-9 | ||
| 035 | |a (OCoLC)36817128 | ||
| 035 | |a (DE-599)BVBBV011726669 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-29 |a DE-703 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA3 | |
| 050 | 0 | |a QC174.26.W28 | |
| 082 | 0 | |a 514/.74 |2 21 | |
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a SK 350 |0 (DE-625)143233: |2 rvk | ||
| 100 | 1 | |a Li, Charles |d 1965- |e Verfasser |0 (DE-588)118039512 |4 aut | |
| 245 | 1 | 0 | |a Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations |c Charles Li ; Stephen Wiggins |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a VIII, 170 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 128 | |
| 500 | |a Literaturverz. S. 161 - 167 | ||
| 650 | 7 | |a Invariants |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 7 | |a Schrödinger, Equation de |2 ram | |
| 650 | 7 | |a Variétés (Mathématiques) |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Invariant manifolds | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Schrödinger equation | |
| 650 | 0 | 7 | |a Nichtlineare Schrödinger-Gleichung |0 (DE-588)4278277-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invariante Mannigfaltigkeit |0 (DE-588)4348147-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Faserung |g Mathematik |0 (DE-588)4472884-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Schrödinger-Gleichung |0 (DE-588)4278277-6 |D s |
| 689 | 0 | 1 | |a Invariante Mannigfaltigkeit |0 (DE-588)4348147-4 |D s |
| 689 | 0 | 2 | |a Faserung |g Mathematik |0 (DE-588)4472884-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wiggins, Stephen |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)1247764664 |4 aut | |
| 830 | 0 | |a Applied mathematical sciences |v 128 |w (DE-604)BV000005274 |9 128 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007909466 | ||
Record in the Search Index
| _version_ | 1804126266495860736 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Invariant Manifolds in Infinite Dimensions 1
1.2 Aims and Scope of This Monograph 9
2 The Perturbed Nonlinear Schrodinger Equation 13
2.1 The Setting for the Perturbed Nonlinear Schrodinger Equation 13
2.2 Spatially Independent Solutions: An Invariant Plane .... 15
2.3 Statement of the Persistence and Fiber Theorems 17
2.4 Explicit Representations for Invariant Manifolds and Fibers 19
2.5 Coordinates Centered on the Resonance Circle 21
2.5.1 Definition of the H Norms 21
2.5.2 A Neighborhood of the Circle of Fixed Points .... 22
2.5.3 An Enlarged Phase Space 23
2.5.4 Scales Through 6 23
2.5.5 The Equations in Their Final Setting 24
2.6 (5 = 0) Invariant Manifolds and the Introduction of a Bump
Function 28
2.6.1 (6 = 0) Invariant Manifolds 28
2.6.2 Tangent and Transversal Bundles of M 29
2.6.3 Introduction of a Bump Function 30
2.6.4 Existence, Smoothness, and Growth Rates for the
Bumped Flow in the Enlarged Phase Space .... 31
3 Persistent Invariant Manifolds 35
3.1 Statement of the Persistence Theorem and the Strategy of
Proof 35
3.2 Proof of the Persistence Theorems 38
3.2.1 Definition of the Graph Transform 38
3.2.2 The Graph Transform as a C° Contraction 42
3.3 The Existence of the Invariant Manifolds 51
3.4 Smoothness of the Invariant Manifolds 52
3.5 Completion of the Proof of the Proposition 61
viii Contents
4 Fibrations of the Persistent Invariant Manifolds 63
4.1 Statement of the Fiber Theorem and the Strategy of Proof 64
4.2 Rate Lemmas 65
4.3 The Existence of an Invariant Subbundle E 73
4.4 Smoothness of the Invariant Subbundle E 78
4.5 Existence of Fibers 89
4.6 Smoothness of the Fiber fE(Q) as a Submanifold 109
4.7 Metric Characterization of the Fibers 117
4.8 Smoothness of Fibers with Respect to the Base Point .... 124
References 161
Index 168
|
| any_adam_object | 1 |
| author | Li, Charles 1965- Wiggins, Stephen ca. 20./21. Jh |
| author_GND | (DE-588)118039512 (DE-588)1247764664 |
| author_facet | Li, Charles 1965- Wiggins, Stephen ca. 20./21. Jh |
| author_role | aut aut |
| author_sort | Li, Charles 1965- |
| author_variant | c l cl s w sw |
| building | Verbundindex |
| bvnumber | BV011726669 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 QC174.26.W28 |
| callnumber-search | QA3 QC174.26.W28 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 350 |
| ctrlnum | (OCoLC)36817128 (DE-599)BVBBV011726669 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02388nam a2200589 cb4500</leader><controlfield tag="001">BV011726669</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220422 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">980113s1997 gw d||| |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">952457016</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387949259</subfield><subfield code="c">Pp. : DM 98.00</subfield><subfield code="9">0-387-94925-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)36817128</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011726669</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA3</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QC174.26.W28</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.74</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 350</subfield><subfield code="0">(DE-625)143233:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Li, Charles</subfield><subfield code="d">1965-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118039512</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations</subfield><subfield code="c">Charles Li ; Stephen Wiggins</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 170 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">128</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 161 - 167</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Invariants</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Physique mathématique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Schrödinger, Equation de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Variétés (Mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematische Physik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Invariant manifolds</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Manifolds (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Schrödinger equation</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Schrödinger-Gleichung</subfield><subfield code="0">(DE-588)4278277-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Invariante Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4348147-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Faserung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4472884-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Schrödinger-Gleichung</subfield><subfield code="0">(DE-588)4278277-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Invariante Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4348147-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Faserung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4472884-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wiggins, Stephen</subfield><subfield code="d">ca. 20./21. Jh.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1247764664</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">128</subfield><subfield code="w">(DE-604)BV000005274</subfield><subfield code="9">128</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007909466</subfield></datafield></record></collection> |
| id | DE-604.BV011726669 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:14:43Z |
| institution | BVB |
| isbn | 0387949259 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007909466 |
| oclc_num | 36817128 |
| open_access_boolean | |
| owner | DE-29 DE-703 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-29 DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | VIII, 170 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Li, Charles 1965- Verfasser (DE-588)118039512 aut Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations Charles Li ; Stephen Wiggins New York [u.a.] Springer 1997 VIII, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 128 Literaturverz. S. 161 - 167 Invariants ram Physique mathématique ram Schrödinger, Equation de ram Variétés (Mathématiques) ram Mathematische Physik Invariant manifolds Manifolds (Mathematics) Mathematical physics Schrödinger equation Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd rswk-swf Faserung Mathematik (DE-588)4472884-0 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s Invariante Mannigfaltigkeit (DE-588)4348147-4 s Faserung Mathematik (DE-588)4472884-0 s DE-604 Wiggins, Stephen ca. 20./21. Jh. Verfasser (DE-588)1247764664 aut Applied mathematical sciences 128 (DE-604)BV000005274 128 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Charles 1965- Wiggins, Stephen ca. 20./21. Jh Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations Applied mathematical sciences Invariants ram Physique mathématique ram Schrödinger, Equation de ram Variétés (Mathématiques) ram Mathematische Physik Invariant manifolds Manifolds (Mathematics) Mathematical physics Schrödinger equation Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd Faserung Mathematik (DE-588)4472884-0 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4348147-4 (DE-588)4472884-0 |
| title | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations |
| title_auth | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations |
| title_exact_search | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations |
| title_full | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations Charles Li ; Stephen Wiggins |
| title_fullStr | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations Charles Li ; Stephen Wiggins |
| title_full_unstemmed | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations Charles Li ; Stephen Wiggins |
| title_short | Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations |
| title_sort | invariant manifolds and fibrations for perturbed nonlinear schrodinger equations |
| topic | Invariants ram Physique mathématique ram Schrödinger, Equation de ram Variétés (Mathématiques) ram Mathematische Physik Invariant manifolds Manifolds (Mathematics) Mathematical physics Schrödinger equation Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd Faserung Mathematik (DE-588)4472884-0 gnd |
| topic_facet | Invariants Physique mathématique Schrödinger, Equation de Variétés (Mathématiques) Mathematische Physik Invariant manifolds Manifolds (Mathematics) Mathematical physics Schrödinger equation Nichtlineare Schrödinger-Gleichung Invariante Mannigfaltigkeit Faserung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007909466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT licharles invariantmanifoldsandfibrationsforperturbednonlinearschrodingerequations AT wigginsstephen invariantmanifoldsandfibrationsforperturbednonlinearschrodingerequations |