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The symmetries of solitons:

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Bibliographische Detailangaben
Beteilige Person:	Palais, Richard S. 1931- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Bonn Univ. 1997
Schriftenreihe:	Vorlesungsreihe / Rheinische Friedrich-Wilhelms-Universität Bonn, Sonderforschungsbereich 256 Nichtlineare Partielle Differentialgleichungen 39
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009939350&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Rudolph-Lipschitz-Vorlesung
Umfang:	II, 80 S.

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Datensatz im Suchindex

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adam_text	RUDOLPH-LIPSCHITZ-LECTURES WINTER SEMESTER 1997 THE SYMMETRIES OF SOLITONS ABSTRACT: IN THESE LECTURES WE WILL EXPOSE THE HIDDEN SOURCES OF THE LARGE GROUPS OF SECRET SYMMETRIES OF THE SO-CALLED SOLITON PDE, SUCH AS KORTEWEG-DE VRIES, NON-LINEAR SCHRODINGER, AND SINE-GORDON. IT IS THESE SYMMETRY GROUPS THAT ARE RESPONSIBLE FOR THE REMARKABLE BEHAVIOR OF THESE SYSTEMS, AND IN PARTICULAR FOR THEIR COMPLETE INTEGRABILITY . WE WILL TAKE AN HISTORICAL APPROACH, STARTING WITH THE PUZZLE PRESENTED BY THE NUMERICAL EXPERIMENTS OF FERMI-PASTA-ULAM, AND THE PARTIAL SOLUTION OF/THAT PUZZLE BY ZABUSKY-KRUSKAL, WHICH MARKED THE ORIGIN OF SOLITON THEORY AS A MATHEMATICAL DISCIPLINE. WE WILL THEN EXPLAIN THE EARLY EXPLANATIONS OF SOLITONS IN TERMS OF INVERSE SCATTERING AND LAX PAIRS, AND FINALLY EXPLAIN HOW THESE IDEAS EVENTUALLY LED TO THE RECENT ELEGANT ELUCIDATION OF SOLITON SYMMETRIES AS DRESSING TRANSFORMATIONS OF LOOP GROUPS. AMS-CLASSIFICATION: SUB Q TTTTLNGEN 205 072 712 58F07, 35Q51, 35Q53, AND 35Q55 RICHARD S. PALAIS DEPARTMENT OF MATHEMATICS BRANDEIS UNIVERSITY WALTHAM, MA 02254-9110 CONTENTS INTRODUCTION 1 REVIEW OF CLASSICAL MECHANICS 4 NEWTON S EQUATIONS 4 THE LAGRANGIAN VIEWPOINT 5 NOETHER S PRINCIPLE 7 THE HAMILTONIAN VIEWPOINT 8 SYMPLECTIC MANIFOLDS 9 EXAMPLES OF CLASSICAL MECHANICAL SYSTEMS 13 PHYSICS NEAR EQUILIBRIUM 15 ERGODICITY AND THERMALIZATION 18 ORIGINS OF SOLITON THEORY 21 THE FERMI-PASTA-ULAM EXPERIMENTS 21 THE KRUSKAL-ZABUSKY EXPERIMENTS 25 A FIRST LOOK AT KDV 29 A SYMPLECTIC STRUCTURE FOR KDV 32 THE INVERSE SCATTERING METHOD 36 LAX EQUATIONS: KDV AS AN ISOSPECTRAL FLOW 38 THE SCATTERING DATA AND ITS EVOLUTION 41 THE INVERSE SCATTERING TRANSFORM 45 AN EXPLICIT FORMULA FOR KDV MULTI-SOLITONS 46 THE KDV HEIRARCHY 47 THE ZS-AKNS SCHEME 50 FLAT CONNECTIONS AND THE LAX EQUATION, ZCC 50 SOME ZS-AKNS EXAMPLES 51 NONLINEAR SCHRODINGER AS A HAMILTONIAN FLOW 53 THE NONLINEAR SCHRODINGER HIERARCHY 56 ZS-AKNS DIRECT SCATTERING THEORY 61 STATEMENTS OF RESULTS 61 OUTLINE OF PROOFS 64 LOOP GROUPS, DRESSING ACTIONS, AND INVERSE SCATTERING 69 SECRET SOURCES OF SOLITON SYMMETRIES 69 TERNG-UHLENBECK FACTORING AND THE DRESSING ACTION 71 THE INVERSE SCATTERING TRANSFORM 72 ZS-AKNS SCATTERING COORDINATES 73 REFERENCES 77 U
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author	Palais, Richard S. 1931-
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spellingShingle	Palais, Richard S. 1931- The symmetries of solitons
title	The symmetries of solitons
title_auth	The symmetries of solitons
title_exact_search	The symmetries of solitons
title_full	The symmetries of solitons Richard S. Palais
title_fullStr	The symmetries of solitons Richard S. Palais
title_full_unstemmed	The symmetries of solitons Richard S. Palais
title_short	The symmetries of solitons
title_sort	the symmetries of solitons
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009939350&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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