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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations: 128 (Applied Mathematical Sciences, 128) - Softcover
Synopsis
This book presents a development of invariant manifold theory for a spe cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.
"synopsis" may belong to another edition of this title.
- PublisherSpringer
- Publication date2012
- ISBN 10 1461273072
- ISBN 13 9781461273073
- BindingPaperback
- LanguageEnglish
- Number of pages180
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (Applied Mathematical Sciences)
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schroedinger Equations
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ISBN 13: 9781461273073
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations
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Springer New York Sep 2012, 2012
ISBN 10: 1461273072
ISBN 13: 9781461273073
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems. 184 pp. Englisch. Seller Inventory # 9781461273073
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations
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Springer New York, Springer US, 2012
ISBN 10: 1461273072
ISBN 13: 9781461273073
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Taschenbuch
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book presents a development of invariant manifold theory for a spe cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work. Seller Inventory # 9781461273073
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schroedinger Equations
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. - Presents detailed and pedagogic proofs - The authors techniques can be applied to a broad class of infinite dimensional dynamical systems - Stephen Wiggins has authored many successful Springer titles and is the editor of Springers Journal of Nonlinear Sc. Seller Inventory # 4189931
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr?dinger Equations
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr?dinger Equations
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations
Published by
Springer New York, Springer US Sep 2012, 2012
ISBN 10: 1461273072
ISBN 13: 9781461273073
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Taschenbuch
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book presents a development of invariant manifold theory for a spe cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and smoothness of locally invariant manifolds. The sec ond part is concerned with fibrations of the stable and unstable manifolds of inflowing and overflowing invariant manifolds. The central technique for proving these results is Hadamard's graph transform method generalized to an infinite-dimensional setting. However, our setting is somewhat different than other approaches to infinite dimensional invariant manifolds since for conservative wave equations many of the interesting invariant manifolds are infinite dimensional and noncom pact. The style of the book is that of providing very detailed proofs of theorems for a specific infinite dimensional dynamical system-the perturbed nonlinear Schrodinger equation. The book is organized as follows. Chapter one gives an introduction which surveys the state of the art of invariant manifold theory for infinite dimensional dynamical systems. Chapter two develops the general setup for the perturbed nonlinear Schrodinger equation. Chapter three gives the proofs of the main results on persistence and smoothness of invariant man ifolds. Chapter four gives the proofs of the main results on persistence and smoothness of fibrations of invariant manifolds. This book is an outgrowth of our work over the past nine years concerning homoclinic chaos in the perturbed nonlinear Schrodinger equation. The theorems in this book provide key building blocks for much of that work.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 184 pp. Englisch. Seller Inventory # 9781461273073
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr?dinger Equations
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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (Applied Mathematical Sciences, 128)
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