Parameterization Method for Unstable Manifolds of Standing Waves on the Line (Q4964242)

scientific article; zbMATH DE number 7315448

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English	Parameterization Method for Unstable Manifolds of Standing Waves on the Line	scientific article; zbMATH DE number 7315448

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instance of

scholarly article

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title

Parameterization Method for Unstable Manifolds of Standing Waves on the Line (English)

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SIAM Journal on Applied Dynamical Systems

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publication date

25 February 2021

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zbMATH Keywords

traveling wave

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parabolic PDE

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stability loss

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invariance equation

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formal series expansion

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Morse index

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describes a project that uses

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SpectrUW: a laboratory for the numerical exploration of spectra of linear operators

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The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces

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The parameterization method for invariant manifolds II: regularity with respect to parameters

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The parameterization method for invariant manifolds. III: Overview and applications

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A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity

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A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms

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A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results

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Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown

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Parameterization Method for Computing Quasi-periodic Reducible Normally Hyperbolic Invariant Tori

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A KAM theory for conformally symplectic systems: efficient algorithms and their validation

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Computation of whiskered invariant tori and their associated manifolds: new fast algorithms

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A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems

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Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case

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Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case.

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A Computational and Geometric Approach to Phase Resetting Curves and Surfaces

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Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence

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Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection

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Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form

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Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

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The parameterization method for invariant manifolds. From rigorous results to effective computations

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Parameterization method for unstable manifolds of delay differential equations

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Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation

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Finite element approximation of invariant manifolds by the parameterization method

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Q4257239

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Šilnikov manifolds in coupled nonlinear Schrödinger equations

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Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation

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Spatiotemporal chaos in terms of unstable recurrent patterns

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Heteroclinic connections in plane Couette flow

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Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations

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Bifurcation computations on an approximate inertial manifold for the 2D Navier-Stokes equations

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Accurate computations on inertial manifolds

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A unified approach to compute foliations, inertial manifolds, and tracking solutions

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The application of centre-manifold theory to the evolution of system which vary slowly in space

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The Utility of an Invariant Manifold Description of the Evolution of a Dynamical System

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A Centre Manifold Description of Contaminant Dispersion in Channels with Varying Flow Properties

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Centre manifolds for infinite dimensional random dynamical systems

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Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction

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Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

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Exact model reduction by a slow-fast decomposition of nonlinear mechanical systems

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Rigorous model reduction for a damped-forced nonlinear beam model: an infinite-dimensional analysis

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Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems

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Computing unstable manifolds of periodic orbits in delay differential equations

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FROM LOCAL TO GLOBAL ONE-DIMENSIONAL UNSTABLE MANIFOLDS IN DELAY DIFFERENTIAL EQUATIONS

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Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays

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Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields

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Spectral and dynamical stability of nonlinear waves

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One-Parameter Semigroups for Linear Evolution Equations

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Evans function computation for the stability of travelling waves

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Alternate Evans functions and viscous shock waves

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Evans function and blow-up methods in critical eigenvalue problems

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EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS

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Exact Homoclinic and Heteroclinic Solutions of the Gray--Scott Model for Autocatalysis

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Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation

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Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach

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Computation of maximal local (un)stable manifold patches by the parameterization method

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A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity

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Computer-assisted proofs for radially symmetric solutions of PDEs

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Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

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Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation

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Numerical proof of stability of viscous shock profiles

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Linear Stability of the Skyrmion

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full work available at URL

https://doi.org/10.1137/19m128243x

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Identifiers

zbMATH Open document ID

1473.74075

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DOI

10.1137/19M128243X

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4964242