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Book Description
The nonlinear Schroedinger (NLS) equation is a fundamental nonlinear partial differential equation (PDE) that arises in many areas and engineering, e.g. in plasma physics, nonlinear waves, and nonlinear optics. It is an example of a completely integrable PDE where phase space structure is known in some detail. 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. The existence and persistence of fibrations of these invariant manifolds is also proved. The authors' techniques are based on an infinite dimensional generalization of the graph transform and can be viewed as an infinite dimensional generalization of Fenichel's results. This book also shows that the authors' techniques are quite general and can be applied to a broad class of infinite dimensional dynamical systems.
Book Info
Presents detailed proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation. DLC: Schrodinger equation.
Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrvdinger Equations (Applied Mathematical Sciences),Charles Li,Kluwer Academic Publishers,0387949259,Applied,Invariant manifolds,Manifolds (Mathematics),Mathematical Physics,Mathematics,Schrodinger equation,Schrèodinger equation,Science,Science/Mathematics,Wave Mechanics,Waves & Wave Mechanics,Applied mathematics,Differential equations,Geometry,Integral equations,Mathematics / Applied,Mathematics / Geometry / General,Topology
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