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Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation

https://doi.org/10.1007/bf03167476
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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/sapm1971504293openalex-snapshot
Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations
inferredcites →https://doi.org/10.1006/jdeq.1993.1022openalex-snapshot
Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields
inferredcites →https://doi.org/10.1007/978-3-642-58058-1openalex-snapshot
C-Xsc: A C++ Class Library for Extended Scientific Computing
inferredcites →https://doi.org/10.1007/978-3-642-61243-5_4openalex-snapshot
Center Manifold Theory in Infinite Dimensions
inferredcites →https://doi.org/10.1007/s002080010010openalex-snapshot
Rigorous Numerics for Partial Differential Equations: The Kuramoto—Sivashinsky Equation
inferredcites →https://doi.org/10.1007/s002110100310openalex-snapshot
Fast verification of solutions of matrix equations
inferredcites →https://doi.org/10.1016/0167-2789(96)00077-2openalex-snapshot
Stable localized solutions of arbitrary length for the quintic Swift-Hohenberg equation
inferredcites →https://doi.org/10.1016/s0167-2789(02)00350-0openalex-snapshot
Solitary wave interaction phenomena in a strut buckling model incorporating restabilisation
inferredcites →https://doi.org/10.1016/s0167-2789(98)00309-1openalex-snapshot
Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian–Hopf bifurcation
inferredcites →https://doi.org/10.1063/1.166142openalex-snapshot
On small stationary localized solutions for the generalized 1-D Swift–Hohenberg equation
inferredcites →https://doi.org/10.1088/0951-7715/8/5/006openalex-snapshot
Attractors for modulation equations on unbounded domains-existence and comparison
inferredcites →https://doi.org/10.1090/cbms/038openalex-snapshot
Isolated Invariant Sets and the Morse Index
inferredcites →https://doi.org/10.1090/mmono/209openalex-snapshot
Far-from-Equilibrium Dynamics
inferredcites →https://doi.org/10.1090/s0002-9947-1985-0797044-3openalex-snapshot
Connected simple systems and the Conley index of isolated invariant sets
inferredcites →https://doi.org/10.1098/rspa.2001.0843openalex-snapshot
Asymptotics of cellular buckling close to the Maxwell load
inferredcites →https://doi.org/10.1137/030600210openalex-snapshot
A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems
inferredcites →https://doi.org/10.1137/040604479openalex-snapshot
Rigorous Numerics for Global Dynamics: A Study of the Swift--Hohenberg Equation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/s10915-013-9749-1openalex-snapshot
Efficient and Generic Algorithm for Rigorous Integration Forward in Time of dPDEs: Part I
inferred← citeshttps://doi.org/10.1007/s10915-024-02785-xopenalex-snapshot
A Rigorous Integrator and Global Existence for Higher-Dimensional Semilinear Parabolic PDEs via Semigroup Theory
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Design and mathematical modeling of polymeric phases to obtain controlled microporosity materials by 3D printing
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An efficient estimate based on FFT in topological verification method
inferred← citeshttps://doi.org/10.1016/j.jde.2024.09.015openalex-snapshot
Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: Constructive proofs of existence
inferred← citeshttps://doi.org/10.1016/j.physd.2007.11.024openalex-snapshot
Periodic and localized states in natural doubly diffusive convection
inferred← citeshttps://doi.org/10.1016/j.physleta.2006.08.072openalex-snapshot
Snakes and ladders: Localized states in the Swift–Hohenberg equation
inferred← citeshttps://doi.org/10.1016/j.physleta.2010.10.010openalex-snapshot
Snaking and isolas of localised states in bistable discrete lattices
inferred← citeshttps://doi.org/10.1080/14689367.2013.790947openalex-snapshot
Exact solutions of the cubic–quintic Swift–Hohenberg equation and their bifurcations
inferred← citeshttps://doi.org/10.1103/physreve.78.046201openalex-snapshot
Eckhaus instability and homoclinic snaking
inferred← citeshttps://doi.org/10.1137/06067794xopenalex-snapshot
Localized Pattern Formation with a Large-Scale Mode: Slanted Snaking
inferred← citeshttps://doi.org/10.1137/080724344openalex-snapshot
Modulated and Localized States in a Finite Domain
inferred← citeshttps://doi.org/10.1137/090762865openalex-snapshot
Localized States in a Model of Pattern Formation in a Vertically Vibrated Layer
inferred← citeshttps://doi.org/10.1137/16m1056006openalex-snapshot
Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
inferred← citeshttps://doi.org/10.21136/am.2018.0082-18openalex-snapshot
Computing discrete convolutions with verified accuracy via Banach algebras and the FFT
inferred← citeshttps://doi.org/10.3390/math7121217openalex-snapshot
Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line
inferred← citeshttps://doi.org/10.3934/dcds.2015.35.4765openalex-snapshot
Rigorous numerics for nonlinear operators with tridiagonal dominant linear part
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