Titlebook: Spectral and Dynamical Stability of Nonlinear Waves; Todd Kapitula,Keith Promislow Textbook 2013 Springer Science+Business Media New York

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书目名称Spectral and Dynamical Stability of Nonlinear Waves网络公开度




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纠缠

The Evans Function for ,th-Order Operators on the Real Line,o not generally have an explicit representation. We sidestep these issues via an analytic extension of the stable and unstable spaces of the asymptotic matrix which leads to the construction of Jost matrices.

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0066-5452 the dynamical systems and functional analysis background of.This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The

ORE

Background Material and Notation,ontext of the Sturm–Liouville theory for second-order operators. These operators have a one-to-one relationship between the ordering of the eigenvalues and the number of zeros for the associated eigenfunctions, which is extremely useful in applications.

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Urgency

Orbital Stability of Waves in Hamiltonian Systems,ps, to interactions of particles in molecular systems. They are also imbued with a rich structure that arises from the conservation of the underlying energy, the Hamiltonian, as well as other quantities such as mass and momentum. In this chapter we present a theory for the nonlinear stability of gen

干涉

Point Spectrum: Reduction to Finite-Rank Eigenvalue Problems,urcation problem begins with an analysis of the point spectrum of the linearized operator associated with the equilibria under investigation. In this chapter we investigate finite-rank bifurcations for which a finite number of point eigenvalues cross the imaginary axis, either transversely or more d

Promotion

Point Spectrum: Linear Hamiltonian Systems,miltonian system, the balance is reflected in the symmetry of the spectrum, which typically pins the essential spectrum to the imaginary axis in unweighted spaces. The mechanism for bifurcation in Hamiltonian systems thus falls upon the point spectrum.

Dysplasia

The Evans Function for Boundary-Value Problems,ructure, as arises from symmetries (Chapter 4.2) and in Hamiltonian systems (Chapter 7). In this chapter we construct the Evans function, an analytic function of the spectral parameter with the property that its zeros correspond to eigenvalues with the order of the zero equal to the algebraic multip