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Modulated and Localized States in a Finite Domain

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What this work says

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

inferredcites →https://doi.org/10.1006/jdeq.1993.1022openalex-snapshot
Perturbed Homoclinic Solutions in Reversible 1:1 Resonance Vector Fields
inferredcites →https://doi.org/10.1007/978-1-4612-1558-5_17openalex-snapshot
Localized Structures In Pattern-Forming Systems
inferredcites →https://doi.org/10.1007/978-1-4612-4574-2openalex-snapshot
Singularities and Groups in Bifurcation Theory
inferredcites →https://doi.org/10.1007/bf03167476openalex-snapshot
Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation
inferredcites →https://doi.org/10.1016/0167-2789(86)90104-1openalex-snapshot
Front motion, metastability and subcritical bifurcations in hydrodynamics
inferredcites →https://doi.org/10.1016/0167-2789(90)90113-4openalex-snapshot
Bifurcation analysis of the Eckhaus instability
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.2007.03.016openalex-snapshot
Computing absolute and essential spectra using continuation
inferredcites →https://doi.org/10.1016/j.physd.2008.10.005openalex-snapshot
Exponential asymptotics of localised patterns and snaking bifurcation diagrams
inferredcites →https://doi.org/10.1016/j.physleta.2006.08.072openalex-snapshot
Snakes and ladders: Localized states in the Swift–Hohenberg equation
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/10.1017/s0022112006002795openalex-snapshot
Localized convection cells in the presence of a vertical magnetic field
inferredcites →https://doi.org/10.1023/a:1008398006403openalex-snapshot
Cellular Buckling in Long Structures
inferredcites →https://doi.org/10.1063/1.1920349openalex-snapshot
Simulations of oscillatory convection in He3–He4 mixtures in moderate aspect ratio containers
inferredcites →https://doi.org/10.1088/0951-7715/21/4/t02openalex-snapshot
Spatially localized structures in dissipative systems: open problems
inferredcites →https://doi.org/10.1088/0951-7715/22/2/013openalex-snapshot
Localized radial solutions of the Swift–Hohenberg equation
inferredcites →https://doi.org/10.1098/rspa.2001.0843openalex-snapshot
Asymptotics of cellular buckling close to the Maxwell load
inferredcites →https://doi.org/10.1103/physreva.38.5461openalex-snapshot
Nonadiabatic effects in convection
inferredcites →https://doi.org/10.1103/physreva.42.7244openalex-snapshot
Domain boundaries in convection patterns
inferredcites →https://doi.org/10.1103/physreve.63.026409openalex-snapshot
Spatiotemporal filamentary patterns in a dc-driven planar gas discharge system
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.73.056211openalex-snapshot
Localized states in the generalized Swift-Hohenberg equation
inferredcites →https://doi.org/10.1103/physreve.78.046201openalex-snapshot
Eckhaus instability and homoclinic snaking
inferredcites →https://doi.org/10.1103/physreve.80.026210openalex-snapshot
Homoclinic snaking in bounded domains
inferredcites →https://doi.org/10.1103/physrevlett.81.333openalex-snapshot
Localization of Waves without Bistability: Worms in Nematic Electroconvection
inferredcites →https://doi.org/10.1103/physrevlett.84.3069openalex-snapshot
Stable Static Localized Structures in One Dimension
inferredcites →https://doi.org/10.1103/physrevlett.92.184501openalex-snapshot
Persistent Holes in a Fluid
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/10.1103/physrevlett.96.214501openalex-snapshot
Localized States in Bistable Pattern-Forming Systems
inferredcites →https://doi.org/10.1103/physrevlett.97.044502openalex-snapshot
Asymptotics of Large Bound States of Localized Structures
inferredcites →https://doi.org/10.1137/06067794xopenalex-snapshot
Localized Pattern Formation with a Large-Scale Mode: Slanted Snaking
inferredcites →https://doi.org/10.1137/070707622openalex-snapshot
Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
inferredcites →https://doi.org/10.1137/080713306openalex-snapshot
Snakes, Ladders, and Isolas of Localized Patterns

What points at this work

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

inferred← citeshttps://doi.org/10.1007/978-3-030-44992-6_12openalex-snapshot
Dissipative Systems
inferred← citeshttps://doi.org/10.1007/s10444-012-9273-0openalex-snapshot
Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations
inferred← citeshttps://doi.org/10.1007/s42985-022-00193-0openalex-snapshot
Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains
inferred← citeshttps://doi.org/10.1016/j.physd.2013.02.005openalex-snapshot
On localised hotspots of an urban crime model
inferred← citeshttps://doi.org/10.1016/j.physd.2020.132735openalex-snapshot
Bistability, wave pinning and localisation in natural reaction–diffusion systems
inferred← citeshttps://doi.org/10.1016/j.physd.2021.132858openalex-snapshot
Dissecting the snake: Transition from localized patterns to spike solutions
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/10.1017/jfm.2013.77openalex-snapshot
Travelling convectons in binary fluid convection
inferred← citeshttps://doi.org/10.1017/s0022112009993144openalex-snapshot
Localized edge states nucleate turbulence in extended plane Couette cells
inferred← citeshttps://doi.org/10.1017/s0022112010004623openalex-snapshot
Convectons, anticonvectons and multiconvectons in binary fluid convection
inferred← citeshttps://doi.org/10.1063/1.3326076openalex-snapshot
Multiple localized states in centrifugally stable rotating flow
inferred← citeshttps://doi.org/10.1063/1.3439672openalex-snapshot
Spatially localized binary fluid convection in a porous medium
inferred← citeshttps://doi.org/10.1063/5.0006126openalex-snapshot
Stripes on finite domains: Why the zigzag instability is only a partial story
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/10.1088/0031-8949/91/2/024003openalex-snapshot
Modulated patterns in a reduced model of a transitional shear flow
inferred← citeshttps://doi.org/10.1088/0169-5983/42/2/025505openalex-snapshot
Convectons in periodic and bounded domains
inferred← citeshttps://doi.org/10.1088/0951-7715/24/12/003openalex-snapshot
Exponential asymptotics of homoclinic snaking
inferred← citeshttps://doi.org/10.1098/rsta.2010.0057openalex-snapshot
The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
inferred← citeshttps://doi.org/10.1103/physreve.100.012204openalex-snapshot
Defectlike structures and localized patterns in the cubic-quintic-septic Swift-Hohenberg equation
inferred← citeshttps://doi.org/10.1103/physreve.80.026210openalex-snapshot
Homoclinic snaking in bounded domains
inferred← citeshttps://doi.org/10.1103/physreve.84.016204openalex-snapshot
Swift-Hohenberg equation with broken cubic-quintic nonlinearity
inferred← citeshttps://doi.org/10.1103/physreve.85.026211openalex-snapshot
Weakly subcritical stationary patterns: Eckhaus instability and homoclinic snaking
inferred← citeshttps://doi.org/10.1103/physreve.85.056307openalex-snapshot
Localized modulation of rotating waves in Taylor-Couette flow
inferred← citeshttps://doi.org/10.1103/physreve.91.043005openalex-snapshot
Localization in a spanwise-extended model of plane Couette flow
inferred← citeshttps://doi.org/10.1103/physreve.97.062221openalex-snapshot
Tristability between stripes, up-hexagons, and down-hexagons and snaking bifurcation branches of spatial connections between up- and down-hexagons
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/10.1137/130918484openalex-snapshot
Numerical Results for Snaking of Patterns over Patterns in Some 2D Selkov--Schnakenberg Reaction-Diffusion Systems
inferred← citeshttps://doi.org/10.1137/140966897openalex-snapshot
Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice
inferred← citeshttps://doi.org/10.1137/16m1093847openalex-snapshot
A Model for Cell Polarization Without Mass Conservation
inferred← citeshttps://doi.org/10.1137/22m1510303openalex-snapshot
Toward Convectons in the Supercritical Regime: Homoclinic Snaking in Natural Doubly Diffusive Convection
inferred← citeshttps://doi.org/10.1146/annurev-conmatphys-031214-014514openalex-snapshot
Spatial Localization in Dissipative Systems
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/proc.2009.2009.109openalex-snapshot
Multipulse states in the Swift-Hohenberg equation
inferred← citeshttps://doi.org/10.48550/arxiv.1809.07847openalex-snapshot
Dissecting the snake: the transition from localized patterns to isolated spikes in pattern formation systems
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