Snakes and ladders: localized states in the Swift-Hohenberg equation
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Publication:942667
DOI10.1016/j.physleta.2006.08.072zbMath1236.35144OpenAlexW2084511990MaRDI QIDQ942667
Publication date: 5 September 2008
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physleta.2006.08.072
Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)
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Cites Work
- Unnamed Item
- Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
- Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
- Cellular buckling in long structures
- Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation
- Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
- A skeleton structure of self-replicating dynamics
- Homoclinic snaking near a heteroclinic cycle in reversible systems
- Localized periodic patterns for the non-symmetric generalized Swift-Hohenberg equation
- Stable particle-like solutions of multidimensional nonlinear fields
- Effects of exponentially small terms in the perturbation approach to localized buckling
- On asymmetric gravity–capillary solitary waves
- Instability of localized buckling modes in a one-dimensional strut model
- Asymptotics of cellular buckling close to the Maxwell load
- Bifurcations of Periodic Solutions Satisfying the Zero-Hamiltonian Constraint in Reversible Differential Equations
- Spatially localized binary-fluid convection
- A new approach to data storage using localized structures
- Magnetohydrodynamic convectons
- Solitary wave interaction phenomena in a strut buckling model incorporating restabilisation
- Three-dimensional magnetohydrodynamic convectons