Availability: Introduction to nonlinear dispersive equations

Introduction to nonlinear dispersive equations:

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Bibliographic Details
Main Authors:	Linares, Felipe (Author), Ponce, Gustavo (Author)
Format:	Book
Language:	English
Published:	New York, NY Springer 2009
Series:	Universitext
Subjects:	Differential equations, Partial Nonlinear wave equations Wellengleichung Nichtlineare partielle Differentialgleichung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016991763&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XI, 256 S.
ISBN:	9780387848983

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MARC


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Record in the Search Index

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adam_text	FELIPE LINARES * GUSTAVO PONCE INTRODUCTION TO NONLINEAR DISPERSIVE EQUATIONS 4Y SPRIN GER CONTENTS THE FOURIER TRANSFORM 1 1.1 THE FOURIER TRANSFORM IN L 1 (K ) 1 1.2 THE FOURIER TRANSFORM IN L 2 (K ) 6 1.3 TEMPERED DISTRIBUTIONS 8 1.4 OSCILLATORY INTEGRALS IN ONE DIMENSION 13 1.5 APPLICATIONS 17 1.6 EXERCISES 18 INTERPOLATION OF OPERATORS. A MULTIPLIER THEOREM 25 2.1 THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1 APPLICATIONS 28 2.2 MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1 APPLICATIONS 33 2.3 THE STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER THEOREM 38 2.5 EXERCISES 39 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL OPERATORS 45 3.1 BASICS 45 3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE BICHARACTERISTIC FLOW 53 3.4 EXERCISES 55 THE LINEAR SCHROEDINGER EQUATION 59 4. 1 BASIC RESULTS 59 4.2 GLOBAL SMOOTHING EFFECTS 64 4.3 LOCAL SMOOTHING EFFECTS 67 4.4 COMMENTS 72 4.5 EXERCISES 84 CONTENTS 1 THE FOURIER TRANSFORM 1 1 .1 THE FOURIER TRANSFORM IN L) (R N ) 1 1.2 THE FOURIER TRANSFORM IN L 2 (M ) 6 1.3 TEMPERED DISTRIBUTIONS 8 1.4 OSCILLATORY INTEGRALS IN ONE DIMENSION 13 1.5 APPLICATIONS 17 1.6 EXERCISES 18 2 INTERPOLATION OF OPERATORS. A MULTIPLIER THEOREM 25 2.1 THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1 APPLICATIONS 28 2.2 MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1 APPLICATIONS 33 2.3 THE STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER THEOREM 38 2.5 EXERCISES 39 3 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL OPERATORS 45 3.1 BASICS 45 3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE BICHARACTERISTIC FLOW 53 3.4 EXERCISES 55 4 THE LINEAR SCHRODINGER EQUATION 59 4.1 BASIC RESULTS 59 4.2 GLOBAL SMOOTHING EFFECTS 64 4.3 LOCAL SMOOTHING EFFECTS 67 4.4 COMMENTS 72 4.5 EXERCISES 84 IX X CONTENTS 5 THE NONLINEAR SCHROEDINGER EQUATION. LOCAL THEORY 89 5.1 L 2 THEORY 91 5.2 H 1 THEORY 99 5.3 H 2 THEORY 103 5.4 COMMENTS 106 5.5 EXERCISES 116 6 ASYMPTOTIC BEHAVIOR FOR NLS EQUATION 119 6.1 GLOBAL RESULTS 119 6.2 FORMATION OF SINGULARITIES 124 6.2.1 CASE A G (1 +4/N,L + 4/(-2)) 126 6.2.2 CASE A = 1 +4/N 128 6.3 COMMENTS 133 6.4 EXERCISES 137 7 KORTEWEG-DE VRIES EQUATION 139 7.1 LINEAR PROPERTIES 141 7.2 MODIFIED KORTEWEG-DE VRIES EQUATION 146 7.3 GENERALIZED KORTEWEG-DE VRIES EQUATION 149 7.4 KORTEWEG-DE VRIES EQUATION 155 7.5 COMMENTS 166 7.6 EXERCISES 170 8 ASYMPTOTIC BEHAVIOR FOR K-GKDV EQUATIONS 173 8.1 CASES K = 1,2,3 174 8.2 CASE * = 4 180 8.3 COMMENTS 185 8.4 EXERCISES 188 9 OTHER NONLINEAR DISPERSIVE MODELS 191 9. 1 DAVEY-STEWARTSON SYSTEMS 191 9.2 ISHIMORI EQUATION 193 9.3 KP EQUATIONS 194 9.4 BO EQUATION 196 9.5 ZAKHAROV SYSTEM 200 9.6 HIGHER ORDER KDV EQUATIONS 203 9.7 EXERCISES 208 10 GENERAL QUASILINEAR SCHROEDINGER EQUATION 211 10.1 THE GENERAL QUASILINEAR SCHROEDINGER EQUATION 211 10.2 COMMENTS 230 10.3 EXERCISES 231 A APPENDIX 233 REFERENCES 239 CONTENTS XI INDEX 255
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author	Linares, Felipe Ponce, Gustavo
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	530 - Physics
dewey-raw	530.124
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discipline	Physik Mathematik
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indexdate	2024-12-20T13:25:07Z
institution	BVB
isbn	9780387848983
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016991763
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owner	DE-703 DE-20 DE-355 DE-BY-UBR DE-29T DE-11 DE-824
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physical	XI, 256 S.
publishDate	2009
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publisher	Springer
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spellingShingle	Linares, Felipe Ponce, Gustavo Introduction to nonlinear dispersive equations Differential equations, Partial Nonlinear wave equations Wellengleichung (DE-588)4065315-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd
subject_GND	(DE-588)4065315-8 (DE-588)4128900-6
title	Introduction to nonlinear dispersive equations
title_auth	Introduction to nonlinear dispersive equations
title_exact_search	Introduction to nonlinear dispersive equations
title_full	Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce
title_fullStr	Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce
title_full_unstemmed	Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce
title_short	Introduction to nonlinear dispersive equations
title_sort	introduction to nonlinear dispersive equations
topic	Differential equations, Partial Nonlinear wave equations Wellengleichung (DE-588)4065315-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd
topic_facet	Differential equations, Partial Nonlinear wave equations Wellengleichung Nichtlineare partielle Differentialgleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016991763&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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