Piecewise-smooth dynamical systems (2008)
Di Bernardo, M., Budd, C. J., Champneys, A. R., Kowalczyk, P.
Bifurcations in Nonsmooth Dynamical Systems (2008)
Di Bernardo, M., Budd, C.J., Champneys, A. R., Kowalczyk, P., Nordmark, A. B., Tost, G. O., ...
A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is...
School of Mathematical Sciences, (2007)
Fengshan Bai, A. R. Champneys, Bath Ba Ay
An extension of an existing truncated boundary-value method for the numerical continuation of connecting orbits is proposed to deal with homoclinic orbits to a saddle-node equilibrium. In contrast to...
Department of Mathematical Sciences, (2007)
global investigation of solitary-wave solutions to a
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
Uni ed derivation of normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems
On Solitary Waves of a Piecewise-Linear Suspension Bridge Model (2007)
A. R. Champneys, P. J. Mckenna
A further investigation of solitary wave solutions is undertaken for a piece-wise linear beam equation which has been proposed as a model for suspension bridges. Solutions are characterized as being...
Yu. A. Kuznetsov, A. R. Champneys, A. R. Champneys
Mathematisch Centrum (SMC), the Dutch foundation
On the stability of solitary wave solutions of the 5th-order KdV equation
Gap solitons in Bragg gratings with a harmonic superlattice (2006)
Yagasaki, K., Merhasin, I. M., Malomed, B. A., Wagenknecht, T., Champneys, A. R.
Solitons are studied in a model of a fiber Bragg grating (BG) whose local reflectivity is subjected to periodic modulation. The superlattice opens an infinite number of new bandgaps in the model's...
Radiationless Travelling Waves In Saturable Nonlinear Schr\"odinger Lattices (2006)
Melvin, T. R. O., Champneys, A. R., Kevrekidis, P. G., Cuevas, J.
The longstanding problem of moving discrete solitary waves in nonlinear Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose...
Accumulation of embedded solitons in systems with quadratic nonlinearity (2005)
Malomed, B. A., Wagenknecht, T., Champneys, A. R., Pearce, M. J.
Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multi-wave systems with quadratic nonlinearity, families of which seem to emerge from a critical point...
A numerical method is set out which efficiently computes stationary (z-independent) two- and three-dimensional spatiotemporal solitons in second-harmonic-generating media. The method relies on a...
Two-parameter nonsmooth bifurcations of limit cycles: classification and open problems (2005)
P. Kowalczyk, M. Di Bernardo, A. R. Champneys, S. J. Hogan, M. Homer, Yu. A. Kuznetsov, ...
This paper proposes a strategy for the classification of codimension-two grazing bifurcations of limit cycles in piecewise smooth systems of ordinary differential equations. Such nonsmooth...
Boundary effects and the onset of Taylor vortices (2004)
Rucklidge, A. M., Champneys, A. R.
It is well established that the onset of spatially periodic vortex states in the Taylor–Couette flow between rotating cylinders occurs at the value of Reynolds number predicted by local bifurcation...
Boundary effects and the onset of Taylor vortices (2004)
Rucklidge, A. M., Champneys, A. R.
It is well established that the onset of spatially periodic vortex states in the Taylor–Couette flow between rotating cylinders occurs at the value of Reynolds number predicted by local bifurcation...
Boundary effects and the onset of Taylor vortices (2004)
Rucklidge, A. M., Champneys, A. R.
It is well established that the onset of spatially periodic vortex states in the Taylor–Couette flow between rotating cylinders occurs at the value of Reynolds number predicted by local bifurcation...
Boundary effects and the onset of Taylor vortices (2003)
Rucklidge, A. M., Champneys, A. R.
It is well established that the onset of spatially periodic vortex states in the Taylor-Couette flow between rotating cylinders occurs at the value of Reynold's number predicted by local bifurcation...
When gap solitons become embedded solitons: a generic unfolding (2003)
Wagenknecht, T., Champneys, A. R.
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...
Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems (2001)
"Embedded solitons": solitary waves in resonance with the linear spectrum (2000)
Champneys, A. R., Malomed, B. A., Yang, J., Kaup, D. J.
It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum...
Cellular buckling in long structures (2000)
Hunt, Giles W., Peletier, M. A., Champneys, A. R., Woods, P. D., Ahmer Wadee, M., Budd, Christopher J, ...
G. J. Lord, A. R. Champneys, G. W. Hunt
Abstract. This paper concerns numerical computation of localised solutions in partial differential equations (PDEs) on unbounded domains. The application is to the von K'arm'an--Donnell...
Multiple Solitary-Waves Due to Second Harmonic Generation in Quadratic Media (1999)
A. C. Yew, A. R. Champneys, P. J. Mckenna
A detailed mathematical analysis is undertaken of solitary wave solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with (2) nonlinearity. The so...
Computation of localized post buckling in long axially--compressed cylindrical shells (1997)
G. J. Lord, A. R. Champneys, G. W. Hunt
Buckling is investigated of a long thin cylindrical shell under longitudinal compression as modelled by the von K'arm'an--Donnell equations. Evidence is reviewed for the buckling being...
A multiplicity of localized buckling modes for twisted rod equations (1996)
The Kirchhoff-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...
A numerical toolbox for homoclinic bifurcation analysis (1996)
A. R. Champneys, Yu. A. Kuznetsov
This paper presents extensions and improvements of recently developed algorithms for the numerical analysis of orbits homoclinic to equilibria in ODEs and describes the implementation of these...
Computation of Homoclinic Solutions to Periodic Orbits in a Reduced Water-wave Problem (1996)
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...
Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system (1994)
B. Buffoni, A. R. Champneys, J. F. Toland, Claverton Down, Ba Ay, U \gamma U
This is a further study of the set of homoclinic solutions (i.e. non-zero solutions asymptotic to 0 as jxj !1) of the reversible Hamiltonian system u iv + Pu 00 + u \Gamma u 2 = 0: () The present...
The Role Of Homoclinic Bifurcations In Understanding The Buckling Of Long Thin Cylindrical Shells
G. J. Lord, A. R. Champneys, G. W. Hunt
. Experiments have shown that long cylinders buckle into localized patterns axially. It is argued that traditional linear or nonlinear analysis is unlikely to capture such modes, nor the effective...
HomCont: An auto86 driver for homoclinic bifurcation analysis. Version 2.0
A. R. Champneys, Yu.A. Kuznetsov, B. Sandstede
HomCont, an auto86-based toolbox for homoclinic bifurcation analysis, is described in detail. The toolbox allows the continuation of codimension-one homoclinic orbits to hyperbolic and non-hyperbolic...