Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (Q992221)

scientific article; zbMATH DE number 5784006

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English	Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics	scientific article; zbMATH DE number 5784006

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instance of

scholarly article

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title

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (English)

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published in

Physica D

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publication date

11 September 2010

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author

Alan R. Champneys

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describes a project that uses

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The inverse scattering transform: Semi-infinite interval

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Stability of pulses on optical fibers with phase-sensitive amplifiers

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Q3768541

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Global uniqueness of homoclinic orbits for a class of fourth order equations

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Homoclinic orbits in the dynamic phase-space analogy of an elastic strut

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Solitary waves with surface tension. I: Trajectories homoclinic to periodic orbits in four dimensions

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Q4953611

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Q4718031

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Exact solitary water waves with capillary ripples at infinity

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Q4165945

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Bifurcation of systems with homoclinic curve of a saddle-focus with saddle quantity zero

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Q4712455

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The solitary wave with surface tension

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The Numerical Computation of Connecting Orbits in Dynamical Systems

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Principles of Localized Buckling for a Strut on an Elastoplastic Foundation

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Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation

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Remarks on finding critical points

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Cascade of homoclinic orbits for Hamiltonian systems: further properties

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Infinitely many large amplitude homoclinic orbits for a class of autonomous Hamiltonian systems

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Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods

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Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system

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A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory

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A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers

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A global condition for quasi-random behavior in a class of conservative systems

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Global existence of homoclinic and periodic orbits for a class of autonomous Hamiltonian systems

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On the stability of solitary wave solutions of the fifth-order KdV equation.

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Solitons due to second harmonic generation

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Perturbation theory for approximately integrable partial differential equations, and the change of amplitude of solitary-wave solutions of the BBM equation

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On the formation of bound states by interacting nonlocal solitary waves

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SUBSIDIARY HOMOCLINIC ORBITS TO A SADDLE-FOCUS FOR REVERSIBLE SYSTEMS

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A global investigation of solitary-wave solutions to a two-parameter model for water waves

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NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS

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A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS

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Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem

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On solitary waves of a piecewise linear suspended beam model

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Hunting for homoclinic orbits in reversible systems: A shooting technique

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A multiplicity of localized buckling modes for twisted rod equations

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Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems

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Multiple solitary waves due to second-harmonic generation in quadratic media

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A Fourier-Series Method for Solving Soliton Problems

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Pathology in dynamical systems. III: Analytic Hamiltonians

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A variational approach to homoclinic orbits in Hamiltonian systems

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Hamiltonian long-wave approximations to the water-wave problem

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Homoclinic twisting bifurcations and cusp horseshoe maps

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Homoclinic orbits in Hamiltonian systems

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Reversible Diffeomorphisms and Flows

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Q4136233

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Capillary–gravity periodic and solitary waves

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Q4344895

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Q5689568

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NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS

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NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS

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A simple global characterization for normal forms of singular vector fields

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COALESCENCE OF REVERSIBLE HOMOCLINIC ORBITS CAUSES ELLIPTIC RESONANCE

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Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points

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Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation

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Solitary waves with damped oscillatory tails: An analysis of the fifth- order Korteweg-de Vries equation

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Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

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Computational aspects of some autonomous differential equations

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Cascades of reversible homoclinic orbits to a saddle-focus equilibrium

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Use of ''simple shooting'' to obtain chaos

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Q3721871

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The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit

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Structural localization phenomena and the dynamical phase-space analogy

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Localized buckling in long axially-loaded cylindrical shells

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Comparative lagrangian formulations for localized buckling

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Localized Elasticae for the Strut on the Linear Foundation

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Existence of perturbed solitary wave solutions to a model equation for water waves

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Stability of solitary waves in dispersive media described by a fifth- order evolution equation

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Q4849849

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Existence d'orbites homoclines à un équilibre elliptique, pour un système réversible

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Q3486279

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Perturbed homoclinic solutions in reversible 1:1 resonance vector fields

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Noose bifurcation of periodic orbits

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Travelling-waves of the Kuramoto-Sivashinsky, equation: period-multiplying bifurcations

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Elements of applied bifurcation theory

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THE "COCOON" BIFURCATIONS IN THREE-DIMENSONAL SYSTEMS WITH TWO FIXED POINTS

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Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus

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Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near \(L_ 2\) in the restricted three-body problem

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The concentration-compactness principle in the calculus of variations. The locally compact case. II

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The concentration-compactness principle in the calculus of variations. The limit case. II

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Homoclinic orbits to small periodic orbits for a class of reversible systems

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Soliton interaction for the extended Korteweg-de Vries equation

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Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems

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Spatially complex equilibria of buckled rods

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Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center

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Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks

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Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders

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Structural stability of the Korteweg-de Vries solitons under a singular perturbation

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Center manifolds for homoclinic solutions

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Instability of localized buckling modes in a one-dimensional strut model

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Existence and stability of \(N\)-pulses on optical fibers with phase-sensitive amplifiers

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Reversible systems

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A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations

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Differentiable dynamical systems

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Variable steps for reversible integration methods

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The Falkner-Skan equation. I: The creation of strange invariant sets

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Subharmonic Branching in Reversible Systems

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Homoclinic period blow-up in reversible and conservative systems

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Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods

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Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature

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Traveling-wave solutions of parabolic systems with discontinuous nonlinear terms

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Global bifurcations and chaos. Analytical methods

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full work available at URL

https://doi.org/10.1016/s0167-2789(97)00209-1

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Identifiers

zbMATH Open document ID

1194.37154

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DOI

10.1016/S0167-2789(97)00209-1

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:992221