Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
type: Item
instance of: scholarly article
title: Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
zbMATH Open document ID: 1194.37154
DOI: 10.1016/S0167-2789(97)00209-1
published in: Physica D
publication date: 2010-09-11T00:00:00Z
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 78A99
zbMATH DE Number: 5784006
author: Alan R. Champneys
describes a project that uses: HomCont
MaRDI profile type: Publication
cites work: The inverse scattering transform: Semi-infinite interval
cites work: Stability of pulses on optical fibers with phase-sensitive amplifiers
cites work: Q3768541
cites work: Global uniqueness of homoclinic orbits for a class of fourth order equations
cites work: Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
cites work: Solitary waves with surface tension. I: Trajectories homoclinic to periodic orbits in four dimensions
cites work: Q4953611
cites work: Q4718031
cites work: Exact solitary water waves with capillary ripples at infinity
cites work: Q4165945
cites work: Bifurcation of systems with homoclinic curve of a saddle-focus with saddle quantity zero
cites work: Q4712455
cites work: The solitary wave with surface tension
cites work: The Numerical Computation of Connecting Orbits in Dynamical Systems
cites work: Principles of Localized Buckling for a Strut on an Elastoplastic Foundation
cites work: Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
cites work: Remarks on finding critical points
cites work: Cascade of homoclinic orbits for Hamiltonian systems: further properties
cites work: Infinitely many large amplitude homoclinic orbits for a class of autonomous Hamiltonian systems
cites work: Periodic and homoclinic orbits for Lorentz-Lagranian systems via variational methods
cites work: Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
cites work: A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory
cites work: A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers
cites work: A global condition for quasi-random behavior in a class of conservative systems
cites work: Global existence of homoclinic and periodic orbits for a class of autonomous Hamiltonian systems
cites work: On the stability of solitary wave solutions of the fifth-order KdV equation.
cites work: Solitons due to second harmonic generation
cites work: Perturbation theory for approximately integrable partial differential equations, and the change of amplitude of solitary-wave solutions of the BBM equation
cites work: On the formation of bound states by interacting nonlocal solitary waves
cites work: SUBSIDIARY HOMOCLINIC ORBITS TO A SADDLE-FOCUS FOR REVERSIBLE SYSTEMS
cites work: A global investigation of solitary-wave solutions to a two-parameter model for water waves
cites work: NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
cites work: A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
cites work: Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
cites work: On solitary waves of a piecewise linear suspended beam model
cites work: Hunting for homoclinic orbits in reversible systems: A shooting technique
cites work: A multiplicity of localized buckling modes for twisted rod equations
cites work: Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems
cites work: Multiple solitary waves due to second-harmonic generation in quadratic media
cites work: Travelling waves in a nonlinearly suspended beam: some computational results and four open questions
cites work: Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
cites work: Q3708354
cites work: A Fourier-Series Method for Solving Soliton Problems
cites work: Pathology in dynamical systems. III: Analytic Hamiltonians
cites work: A variational approach to homoclinic orbits in Hamiltonian systems
cites work: Hamiltonian long-wave approximations to the water-wave problem
cites work: Homoclinic twisting bifurcations and cusp horseshoe maps
cites work: Homoclinic orbits in Hamiltonian systems
cites work: Reversible Diffeomorphisms and Flows
cites work: Q4136233
cites work: Capillary–gravity periodic and solitary waves
cites work: Q4344895
cites work: Q5689568
cites work: NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
cites work: NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
cites work: A simple global characterization for normal forms of singular vector fields
cites work: COALESCENCE OF REVERSIBLE HOMOCLINIC ORBITS CAUSES ELLIPTIC RESONANCE
cites work: Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
cites work: Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation
cites work: Solitary waves with damped oscillatory tails: An analysis of the fifth- order Korteweg-de Vries equation
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Computational aspects of some autonomous differential equations
cites work: Cascades of reversible homoclinic orbits to a saddle-focus equilibrium
cites work: Use of ''simple shooting'' to obtain chaos

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3721871

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Structural localization phenomena and the dynamical phase-space analogy

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Localized buckling in long axially-loaded cylindrical shells

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Comparative lagrangian formulations for localized buckling

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Localized Elasticae for the Strut on the Linear Foundation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence of perturbed solitary wave solutions to a model equation for water waves

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Stability of solitary waves in dispersive media described by a fifth- order evolution equation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q4849849

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence d'orbites homoclines à un équilibre elliptique, pour un système réversible

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3486279

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Water waves for small surface tension: an approach via normal form

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Perturbed homoclinic solutions in reversible 1:1 resonance vector fields

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Noose bifurcation of periodic orbits

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Travelling-waves of the Kuramoto-Sivashinsky, equation: period-multiplying bifurcations

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence of solitary waves for water-wave models

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Nonlinearly Resonant Surface Waves and Homoclinic Bifurcation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3138991

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Bifurcation of degenerate homoclinic orbits in reversible and conservative systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: FAMILIES OF TRANSVERSE POINCARÉ HOMOCLINIC ORBITS IN 2N-DIMENSIONAL HAMILTONIAN SYSTEMS CLOSE TO THE SYSTEM WITH A LOOP TO A SADDLE-CENTER

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Stability of Pulses in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Elements of applied bifurcation theory

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: THE "COCOON" BIFURCATIONS IN THREE-DIMENSONAL SYSTEMS WITH TWO FIXED POINTS

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3978425

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near \(L_ 2\) in the restricted three-body problem

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Using Melnikov's method to solve Silnikov's problems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: The concentration-compactness principle in the calculus of variations. The locally compact case. II

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: The concentration-compactness principle in the calculus of variations. The limit case. II

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Homoclinic orbits to small periodic orbits for a class of reversible systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Computation of localized post buckling in long axially compressed cylindrical shells

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q4718039

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Soliton interaction for the extended Korteweg-de Vries equation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Travelling Waves in a Suspension Bridge

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Steady solutions of the Kuramoto-Sivashinsky equation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Spatially complex equilibria of buckled rods

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Structural stability of the Korteweg-de Vries solitons under a singular perturbation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q4867883

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Center manifolds for homoclinic solutions

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Instability of localized buckling modes in a one-dimensional strut model

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence and stability of \(N\)-pulses on optical fibers with phase-sensitive amplifiers

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Reversible systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q5509205

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Differentiable dynamical systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Variable steps for reversible integration methods

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Existence of a generalized solitary wave solution for water with positive Bond number less than 1/3

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: The Falkner-Skan equation. I: The creation of strange invariant sets

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: From helix to localized writhing in the torsional post-buckling of elastic rods

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3031670

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Subharmonic Branching in Reversible Systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Homoclinic period blow-up in reversible and conservative systems

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Traveling-wave solutions of parabolic systems with discontinuous nonlinear terms

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Global bifurcations and chaos. Analytical methods

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Q3334229

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: On asymmetric gravity–capillary solitary waves

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (cites work)
cites work: Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (full work available at URL)
full work available at URL: s0167-2789(97)00209-1

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (OpenAlex ID)
OpenAlex ID: W2136143898