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Snakes and ladders: Localized states in the Swift–Hohenberg equation

https://doi.org/10.1016/j.physleta.2006.08.072
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields
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Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation
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Partial Differential Equations
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Front motion, metastability and subcritical bifurcations in hydrodynamics
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Stable particle-like solutions of multidimensional nonlinear fields
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/j.physd.2005.04.018openalex-snapshot
Homoclinic snaking near a heteroclinic cycle in reversible systems
inferredcites →https://doi.org/10.1016/j.physd.2005.06.009openalex-snapshot
Localized periodic patterns for the non-symmetric generalized 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(97)00209-1openalex-snapshot
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
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/10.1016/s0167-2789(99)00010-xopenalex-snapshot
A skeleton structure of self-replicating dynamics
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Three-dimensional magnetohydrodynamic convectons
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Magnetohydrodynamic convectons
inferredcites →https://doi.org/10.1017/s0022112006000759openalex-snapshot
Spatially localized binary-fluid convection
inferredcites →https://doi.org/10.1017/s0022112096003643openalex-snapshot
On asymmetric gravity–capillary solitary waves
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Cellular Buckling in Long Structures
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Experimental observation of self-replicating spots in a reaction–diffusion system
inferredcites →https://doi.org/10.1038/382793a0openalex-snapshot
Localized excitations in a vertically vibrated granular layer
inferredcites →https://doi.org/10.1063/1.1642311openalex-snapshot
A new approach to data storage using localized structures
inferredcites →https://doi.org/10.1098/rspa.1999.0407openalex-snapshot
Effects of exponentially small terms in the perturbation approach to localized buckling
inferredcites →https://doi.org/10.1098/rspa.2001.0843openalex-snapshot
Asymptotics of cellular buckling close to the Maxwell load
inferredcites →https://doi.org/10.1098/rsta.1997.0111openalex-snapshot
Instability of localized buckling modes in a one-dimensional strut model
inferredcites →https://doi.org/10.1103/physreva.38.5461openalex-snapshot
Nonadiabatic effects in convection
inferredcites →https://doi.org/10.1103/physreve.51.2046openalex-snapshot
Pattern selection in the generalized Swift-Hohenberg model
inferredcites →https://doi.org/10.1103/physreve.57.524openalex-snapshot
Confined states in large-aspect-ratio thermosolutal convection
inferredcites →https://doi.org/10.1103/physreve.65.046606openalex-snapshot
Two-dimensional clusters of solitary structures in driven optical cavities
inferredcites →https://doi.org/10.1103/physreve.66.046606openalex-snapshot
Computationally determined existence and stability of transverse structures. II. Multipeaked cavity solitons
inferredcites →https://doi.org/10.1103/physreve.68.056605openalex-snapshot
Multistable pulselike solutions in a parametrically driven Ginzburg-Landau equation
inferredcites →https://doi.org/10.1103/physreve.73.056211openalex-snapshot
Localized states in the generalized Swift-Hohenberg equation
inferredcites →https://doi.org/10.1103/physrevlett.83.3190openalex-snapshot
Oscillons and Propagating Solitary Waves in a Vertically Vibrated Colloidal Suspension
inferredcites →https://doi.org/10.1103/physrevlett.84.3069openalex-snapshot
Stable Static Localized Structures in One Dimension
inferredcites →https://doi.org/10.1103/physrevlett.94.184503openalex-snapshot
Two-Dimensional Solitons on the Surface of Magnetic Fluids
inferredcites →https://doi.org/10.1103/physrevlett.95.244501openalex-snapshot
Simulations of Localized States of Stationary Convection in He 3 − He 4 Mixtures
inferredcites →https://doi.org/10.1137/s0036141002418637openalex-snapshot
Bifurcations of Periodic Solutions Satisfying the Zero-Hamiltonian Constraint in Reversible Differential Equations

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

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Proposed Resolution of Theory-Experiment Discrepancy in Homoclinic Snaking
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Localized plumes in three-dimensional compressible magnetoconvection
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Localized Structures in the Multi-dimensional Swift-Hohenberg Equation
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