Results
author = "Champneys, AR"
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
Author(s) :
Champneys, AR
Description :
This survey article reviews the theory and application of homoclinic orbits to equilibria in reversible continuous-time dynamical systems, where the homoclinic orbit and the equilibrium are both reversible. The focus is on even-order reversible systems in four or more dimensions. Local theory, gen...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
Homoclinic orbits in reversible systems II : multi-bumps and saddle-centres
Author(s) :
Champneys, AR
Description :
This article extends a review by the author in Physica D, vol.112, pp.158-186 of the theory and application of homoclinic orbits to equilibria in even-order, time-reversible systems of autonomous ordinary differential equations, either Hamiltonian or not. Recent results in two directions are su...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems
Author(s) :
Champneys, AR
Description :
The persistence from a singular limit is studied of homoclinic orbits to a saddle-centre equilibrium in four-dimensional reversible vector fields. The linearisation is assumed to have eigenvalues +i omega, -i omega, + lambda and - lambda, lambda and omega >0, with the singular limit being lambda ->...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
When gap solitons become embedded solitons : an unfolding via Lin's method
Description :
A two-parameter unfolding is considered of single-pulsed homoclinic orbits to an equilibrium with two real and two zero eigenvalues in fourth-order reversible dynamical systems. One parameter controls the linearisation, with a transition occurring between a saddle-centre and a hyperbolic equilibrium...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
Discrete snaking: multiple cavity solitons in saturable media
Description :
A one-dimensional lattice equation is studied that models the light field in an optical system comprised of a periodic array of optical cavities pumped by a coherent light source. The model includes effects of linear detuning, linear and nonlinear dissipation and saturable nonlinearity. A wide varie...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities
Description :
This paper continues an investigation into a one-dimensional lattice equation that models the light field in a system comprised of a periodic array of pumped optical cavities with saturable nonlinearity. The additional effects of a spatial gradient of the phase of the pump field are studied, which i...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
On the stability of solitary wave solutions of the 5th-order KdV equation
Description :
The Korteweg-de Vries equation with a fifth-order-derivative dispersive perturbation has been used as a model for a variety of physical phenomena including gravity-capillary water waves. It has recently been shown that this equation possesses infinitely many multi-pulsed stationary solitary wave so...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
A global investigation of solitary-wave solutions to a two-parameter model for water waves
Description :
The model equation (2r''''/15)-(br'')+(ar)+(3r^2/2)-((r')^2/2)+[rr']'=0 arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravitycapillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
A multiplicity of localised buckling modes for twisted rod equations
Description :
The Kirchho-Love equations governing the spatial equilibria of long thin elastic rods subject to end tension and moment are reviewed and used to examine the existence of localized buckling solutions. The effects of shear and axial extension are not considered, but the model does additionally allow ...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English
Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
Description :
This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at infinit...
Repository :
Bristol Repository of Scholarly Eprints (ROSE)
Language(s) :
English