Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations
نام عام مواد
[Book]
نام نخستين پديدآور
by Charles Li, Stephen Wiggins.
وضعیت نشر و پخش و غیره
محل نشرو پخش و غیره
New York, NY :
نام ناشر، پخش کننده و غيره
Imprint: Springer,
تاریخ نشرو بخش و غیره
1997.
فروست
عنوان فروست
Applied Mathematical Sciences,
مشخصه جلد
128
شاپا ي ISSN فروست
0066-5452 ;
یادداشتهای مربوط به مندرجات
متن يادداشت
1 Introduction -- 1.1 Invariant Manifolds in Infinite Dimensions -- 1.2 Aims and Scope of This Monograph -- 2 The Perturbed Nonlinear Schrödinger Equation -- 2.1 The Setting for the Perturbed Nonlinear Schrödinger Equation -- 2.2 Spatially Independent Solutions: An Invariant Plane -- 2.3 Statement of the Persistence and Fiber Theorems -- 2.4 Explicit Representations for Invariant Manifolds and Fibers -- 2.5 Coordinates Centered on the Resonance Circle -- 2.6 (6 = 0) Invariant Manifolds and the Introduction of a Bump Function -- 3 Persistent Invariant Manifolds -- 3.1 Statement of the Persistence Theorem and the Strategy of Proof -- 3.2 Proof of the Persistence Theorems -- 3.3 The Existence of the Invariant Manifolds -- 3.4 Smoothness of the Invariant Manifolds -- 3.5 Completion of the Proof of the Proposition -- 4 Fibrations of the Persistent Invariant Manifolds -- 4.1 Statement of the Fiber Theorem and the Strategy of Proof -- 4.2 Rate Lemmas -- 4.3 The Existence of an Invariant Subbundle E -- 4.4 Smoothness of the Invariant Subbundle E -- 4.5 Existence of Fibers -- 4.6 Smoothness of the Fiber fE(Q) as a Submanifold -- 4.7 Metric Characterization of the Fibers -- 4.8 Smoothness of Fibers with Respect to the Base Point -- References.
بدون عنوان
0
یادداشتهای مربوط به خلاصه یا چکیده
متن يادداشت
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.
ویراست دیگر از اثر در قالب دیگر رسانه
شماره استاندارد بين المللي کتاب و موسيقي
9781461273073
قطعه
عنوان
Springer eBooks
موضوع (اسم عام یاعبارت اسمی عام)
موضوع مستند نشده
Cell aggregation-- Mathematics.
موضوع مستند نشده
Geometry.
موضوع مستند نشده
Global analysis (Mathematics).
موضوع مستند نشده
Mathematics.
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )