The nonlinear Schrödinger equation: singular solutions and optical collapse
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2015
|
| Series: | Applied Mathematical Sciences
192 |
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (XXXI, 862 S.) 202 illus., 100 illus. in color |
| ISBN: | 9783319127484 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-3-319-12748-4 |
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Record in the Search Index
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| adam_text | THE NONLINEAR SCHROEDINGER EQUATION
/ FIBICH, GADI
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
DERIVATION OF THE NLS
LINEAR PROPAGATION
EARLY SELF-FOCUSING RESEARCH
NLS MODELS
EXISTENCE OF NLS SOLUTIONS
SOLITARY WAVES
VARIANCE IDENTITY
SYMMETRIES AND THE LENS TRANSFORMATION
STABILITY OF SOLITARY WAVES
THE EXPLICIT CRITICAL SINGULAR PEAK-TYPE SOLUTION
THE EXPLICIT CRITICAL SINGULAR RING-TYPE SOLUTION
THE EXPLICIT SUPERCRITICAL SINGULAR PEAK-TYPE SOLUTION
BLOWUP RATE, BLOWUP PROFILE, AND POWER CONCENTRATION
THE PEAK-TYPE BLOWUP PROFILE
VORTEX SOLUTIONS
NLS ON A BOUNDED DOMAIN
DERIVATION OF REDUCED EQUATIONS
LOGLOG LAW AND ADIABATIC COLLAPSE
SINGULAR H1 RING-TYPE SOLUTIONS
SINGULAR H1 VORTEX SOLUTIONS
SINGULAR H1 PEAK-TYPE SOLUTIONS
SINGULAR STANDING-RING SOLUTIONS
SINGULAR SHRINKING-RING SOLUTIONS
CRITICAL AND THRESHOLD POWERS FOR COLLAPSE
MULTIPLE FILAMENTATION
NONLINEAR GEOMETRICAL OPTICS (NGO) METHOD
LOCATION OF SINGULARITY
COMPUTATION OF SOLITARY WAVES
NUMERICAL METHODS FOR THE NLS
EFFECTS OF SPATIAL DISCRETIZATION
MODULATION THEORY
CUBIC-QUINTIC AND SATURATED NONLINEARITIES
LINEAR AND NONLINEAR DAMPING
NONPARAXIALITY AND BACKSCATTERING (NONLINEAR HELMHOLTZ EQUATION)
ULTRASHORT PULSES
NORMAL AND ANOMALOUS DISPERSION
NGO METHOD FOR ULTRASHORT PULSES WITH ANOMALOUS DISPERSION
CONTINUATIONS BEYOND THE SINGULARITY
LOSS OF PHASE AND CHAOTIC INTERACTIONS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
THE NONLINEAR SCHROEDINGER EQUATION
/ FIBICH, GADI
: 2015
ABSTRACT / INHALTSTEXT
THIS BOOK IS AN INTERDISCIPLINARY INTRODUCTION TO OPTICAL COLLAPSE OF
LASER BEAMS, WHICH IS MODELLED BY SINGULAR (BLOW-UP) SOLUTIONS OF THE
NONLINEAR SCHROEDINGER EQUATION. WITH GREAT CARE AND DETAIL, IT DEVELOPS
THE SUBJECT INCLUDING THE MATHEMATICAL AND PHYSICAL BACKGROUND AND THE
HISTORY OF THE SUBJECT. IT COMBINES RIGOROUS ANALYSIS, ASYMPTOTIC
ANALYSIS, INFORMAL ARGUMENTS, NUMERICAL SIMULATIONS, PHYSICAL MODELLING,
AND PHYSICAL EXPERIMENTS. IT REPEATEDLY EMPHASIZES THE RELATIONS BETWEEN
THESE APPROACHES, AND THE INTUITION BEHIND THE RESULTS. THE NONLINEAR
SCHROEDINGER EQUATION WILL BE USEFUL TO GRADUATE STUDENTS AND
RESEARCHERS IN APPLIED MATHEMATICS WHO ARE INTERESTED IN SINGULAR
SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS, NONLINEAR OPTICS AND
NONLINEAR WAVES, AND TO GRADUATE STUDENTS AND RESEARCHERS IN PHYSICS AND
ENGINEERING WHO ARE INTERESTED IN NONLINEAR OPTICS AND BOSE-EINSTEIN
CONDENSATES. IT CAN BE USED FOR COURSES ON PARTIAL DIFFERENTIAL
EQUATIONS, NONLINEAR WAVES, AND NONLINEAR OPTICS. GADI FIBICH IS A
PROFESSOR OF APPLIED MATHEMATICS AT TEL AVIV UNIVERSITY. “THIS BOOK
PROVIDES A CLEAR PRESENTATION OF THE NONLINEAR SCHRODINGER EQUATION AND
ITS APPLICATIONS FROM VARIOUS PERSPECTIVES (RIGOROUS ANALYSIS, INFORMAL
ANALYSIS, AND PHYSICS). IT WILL BE EXTREMELY USEFUL FOR STUDENTS AND
RESEARCHERS WHO ENTER THIS FIELD.” FRANK MERLE, UNIVERSITE DE
CERGY-PONTOISE AND INSTITUT DES HAUTES ETUDES SCIENTIFIQUES, FRANCE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Fibich, Gadi |
| author_GND | (DE-588)129177776 |
| author_facet | Fibich, Gadi |
| author_role | aut |
| author_sort | Fibich, Gadi |
| author_variant | g f gf |
| building | Verbundindex |
| bvnumber | BV042481725 |
| classification_rvk | UK 1200 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)906182977 (DE-599)BVBBV042481725 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-3-319-12748-4 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:23:00Z |
| institution | BVB |
| isbn | 9783319127484 |
| issn | 0066-5452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027916684 |
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| spelling | Fibich, Gadi Verfasser (DE-588)129177776 aut The nonlinear Schrödinger equation singular solutions and optical collapse Gadi Fibich Cham [u.a.] Springer 2015 1 Online-Ressource (XXXI, 862 S.) 202 illus., 100 illus. in color txt rdacontent c rdamedia cr rdacarrier Applied mathematical sciences 192 0066-5452 Mathematics Differential equations, partial Partial Differential Equations Mathematical Applications in the Physical Sciences Mathematical Physics Atomic, Molecular, Optical and Plasma Physics Optics and Electrodynamics Nonlinear Dynamics Mathematik Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-3-319-12747-7 Applied Mathematical Sciences 192 (DE-604)BV040244599 192 https://doi.org/10.1007/978-3-319-12748-4 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027916684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027916684&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fibich, Gadi The nonlinear Schrödinger equation singular solutions and optical collapse Applied Mathematical Sciences Mathematics Differential equations, partial Partial Differential Equations Mathematical Applications in the Physical Sciences Mathematical Physics Atomic, Molecular, Optical and Plasma Physics Optics and Electrodynamics Nonlinear Dynamics Mathematik Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4278277-6 (DE-588)4053332-3 (DE-588)4128900-6 |
| title | The nonlinear Schrödinger equation singular solutions and optical collapse |
| title_auth | The nonlinear Schrödinger equation singular solutions and optical collapse |
| title_exact_search | The nonlinear Schrödinger equation singular solutions and optical collapse |
| title_full | The nonlinear Schrödinger equation singular solutions and optical collapse Gadi Fibich |
| title_fullStr | The nonlinear Schrödinger equation singular solutions and optical collapse Gadi Fibich |
| title_full_unstemmed | The nonlinear Schrödinger equation singular solutions and optical collapse Gadi Fibich |
| title_short | The nonlinear Schrödinger equation |
| title_sort | the nonlinear schrodinger equation singular solutions and optical collapse |
| title_sub | singular solutions and optical collapse |
| topic | Mathematics Differential equations, partial Partial Differential Equations Mathematical Applications in the Physical Sciences Mathematical Physics Atomic, Molecular, Optical and Plasma Physics Optics and Electrodynamics Nonlinear Dynamics Mathematik Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Mathematics Differential equations, partial Partial Differential Equations Mathematical Applications in the Physical Sciences Mathematical Physics Atomic, Molecular, Optical and Plasma Physics Optics and Electrodynamics Nonlinear Dynamics Mathematik Nichtlineare Schrödinger-Gleichung Schrödinger-Gleichung Nichtlineare partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-3-319-12748-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027916684&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027916684&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT fibichgadi thenonlinearschrodingerequationsingularsolutionsandopticalcollapse |