Publications of Alan Champneys
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Publications of Alan Champneys 1991-2002
(Last updated March 2002)
Note that you can browse the abstracts of all preprint versions since 1997
with an option to download. Just follow the links below.
Some older papers are also down available as
downloadable preprints
- [B1] Champneys, A.R., Hunt G.H. and Thompson, J.M.T. (Eds.) 1999
Localization and solitary waves in solid mechanics.
World Scientific Advanced Series in Nonlinear Dynamics. Volume 12.
396 pages.
- [1] Champneys, A.R. 1991 Homoclinic orbits in the dynamics of
articulated pipes conveying fluid. Nonlinearity 4, 747--774.
- [2] Champneys, A.R. 1993 Homoclinic tangencies in the dynamics of
articulated pipes conveying fluid. Physica D 62,
347-359.
- [3] Champneys, A.R. & Spence, A. 1993 Hunting for homoclinic orbits in
reversible systems; a shooting technique. Advances in Computational
Mathematics 1, 81-108.
- [4] Champneys, A.R. & Toland, J.F. 1993 Bifurcation of a plethora of
multi-modal homoclinic orbits for autonomous Hamiltonian systems.
Nonlinearity 6, 665-721.
- [5] Champneys, A.R. and Kuznetsov, Yu.A. 1994 Numerical detection and
continuation of codimension-two homoclinic orbits. International
Journal of Bifurcation and Chaos, 4, 785-822.
- [6] Champneys, A.R. 1994 Subsidiary homoclinic orbits to a saddle-focus
for reversible systems. International Journal of Bifurcation and
Chaos 4, 1447-1482.
- [7] Champneys, A.R., Harris, S., Toland, J., Warren, J. & Williams, D.
1995 Algebra, analysis and probability for a coupled system of reaction
diffusion equations. Philosophical Transactions of the Royal
Society of London A 350, 69-112.
- [8] Roose, D., Lust, K., Champneys, A., & Spence, A. 1995 A Newton-Picard
shooting method for computing periodic solutions of large-scale
dynamical systems. Chaos, Solitons and Fractals
5 1913-1925.
- [9] Thompson, J.M.T. & Champneys, A.R. 1996 From helix to localised
writhing in the torsional postbuckling of elastic rods. Proceedings
of the Royal Soceity of London A 452 117-138.
- [10] Champneys, A.R., Haerterich, J. & Sandstede, B. 1996 A
non-transverse homoclinic orbit to a saddle-node equilibrium.
Ergodic Theory and Dynamical Systems 16 431-450.
- [11] Buffoni, B., Champneys, A.R. & Toland, J.F. 1996 Bifurcation
and coalescence of a plethora of multi-modal homoclinic orbits in
a Hamiltonian system. Journal of Dynamics and Differential Equations
8 221-281.
- [12] Champneys, A.R. & Thompson, J.M.T. 1996 A multiplicity of
localised buckling modes for twisted rod equations. Proceedings of
the Royal Society of London A 452 , 2467-2491.
- [13] Champneys, A.R., Kuznetsov, Yu.A. & Sandstede, B. 1996
A numerical toolbox for homoclinic bifurcation analysis.
International Journal of Bifurcation and Chaos 6, 867-887.
- [14] Bai, F. & Champneys, A.R. 1996 Numerical computation of
saddle-node homoclinic orbits of co-dimension one and two.
Journal of Dynamics and Stability of Systems 11 , 327-348.
- [15] Champneys, A.R. & Lord, G.J. 1997 Computation of homoclinic
solutions to periodic orbits in a reduced water-wave problem.
Physica D 102 , 101-124.
- [16] Champneys, A.R. & Groves, M.D. 1997 A global investigation
of a solitary wave solutions to a fifth-order two-parameter model
equation for water waves. Journal of Fluid Mechanics
342 , 199-229.
- [17] Champneys, A.R. & McKenna, P.J. 1997
On solitary waves of a piece-wise linear suspended beam model.
Nonlinearity 10 , 1763-1782.
- [18] Buryak, A.V. & Champneys, A.R. 1997 On the stability of
solitary waves solutions to the 5th-order KdV equation.
Physics Letters A 233 , 58-62.
- [19] Lord G.J., Champneys A.R. & Hunt, G.W. 1997 Computation of
localised post-buckling in long axially compressed cylindrical shells.
Philosphiocal Transactions of the Royal Society of London A
355 , 2137-2150.
Abstract & preprint;
- [20] Champneys, A.R., van der Heijden, G.H.M. & Thompson, J.M.T 1997
Spatially complex localization after one-twist-per-wave equilibria
in twisted circular rods with initial curvature.
Philosphiocal Transactions of the Royal Society of London A
355 , 2151-2174.
Abstract & preprint;
- [21] Champneys, A.R. 1998 Homoclinic orbits in reversible systems
and their applications in mechanics, fluids and optics
Physica D 112 , 158-186.
- [22] Lust, K., Roose, D., Spence, A. & Champneys, A.R. 1998
An adaptive Newton-Picard algorithm with subspace iteration for
computing periodic solutions. SIAM Journal of Scientific
Computation , 19 , 1188-1209.
- [23] Champneys, A.R., Malomed, B. & Friedman M.J. 1998 Thirring
solitons in the presensce of dispersion.
Physical Review Letters , 80 4168-4171.
Abstract & preprint;
- [24] di Bernardo, M., Budd, C.J. & Champneys, A.R. 1998 Analysis
of non-smooth dynamics of the DC/DC Buck Converter.
Nonlinearity 11 859-890.
Abstract & preprint;
- [25] van der Heijden, G.H.M., Champneys, A.R. & Thompson, J.M.T.
1998 The spatial complexity of localised buckling in rods with
non-circular cross-section. SIAM Journal of Applied Mathematics
, 59 198-221.
- [26] Lowenberg, M.H. & Champneys, A.R, 1988
Shil'nikov homoclinic dynamics and the escape from roll autorotation in an
F-4 model. Phil. Trans. Roy. Soc. Lond. A , 356 2241-2256.
Abstract & preprint;
- [27] Kivshar, Yu.S., Champneys, A.R, Cai D. & Bishop, A.R. 1988
Multiple states of intrinsic localized modes.
Physical Review B. , 58 5423-5428.
Abstract & preprint.
- [28] Yew, A.C., Champneys, A.R. & McKenna, P.J. 1999 Localised
solutions of a coupled first and second harmonic nonlinear
Shroedinger system. Journal of Nonlinear Science , 9 , 33-52.
Abstract & preprint;
- [29] van der Heijden, G.H.M., Champneys, A.R. &
Thompson J.M.T. 1999 On twisted elastic rods constrained to lie in the plane.
J. Mech. Phys. Solids 47 59-79.
- [30] Champneys, A.R. & Rodriguez-Luis, A.J. 1999 A non-transverse
Shilnikov-Hopf bifurcation; the uncoupling of homoclinic orbits
and homoclinic tangencies.
Physica D 128 130-158.
Abstract & preprint;
- [31] Hunt, G.W., Lord, G.J. & Champneys, A.R. 1999
Homoclinic and heteroclinic orbits underlying
the post-buckling of axially-compressed cylindrical shells.
Computer Methods in Applied Mechanics and Engineering
170 239-251.
Abstract & preprint;
- [32] Woods, P.D. & Champneys, A.R. 1999
Heteroclinic tangles and homoclinic snaking in the unfolding
of a degenerate reversible Hamiltonian Hopf bifurcation.
Physica D 129 147-170.
Abstract & preprint;
- [33] Lord, G.J., Champneys, A.R. & Hunt, G.W. 1999 Computation of
homoclinic orbits in partial differential equations: an applicaiton to
cylindrical shell buckling. SIAM J. Sci. Comp.
21 591-619.
- [34] Champneys, A.R. 1999
Homoclinic orbits in reversible systems II:
Multi-bumps and saddle-centres. CWI Quarterly 12
185-212.
Abstract & preprint;
- [35] Champnyes A.R. & Malomed, B.A. 1999 Moving embedded solitons.
J. Phys. A 32 L547-553.
Abstract & preprint;
- [36] Champneys A.R. & Malomed, B.A. 2000
Embedded solitons in a three-wave system
Phys. Rev. E 61 886-890.
Abstract & preprint;
- [37] Skryabin, D.V, Champneys, A.R. & Firth W.J. 2000
Frequency selection
by soliton excitation in nondegenerate intracavity downconversion.
Phys. Rev. Lett. 84 463-466.
Abstract & preprint
- [38] Hunt, G.W., Peletier, M.A., Champneys, A.R., Woods, P.D.,
Wadee, M.Ahmer, Budd, C.J. & Lord G.J. 2000
Cellular Buckling in Long Structures
Nonlinear Dynamics 21 3-29.
Abstract & preprint;
- [39] Champneys, A.R., McKenna, P.J. & Zegeling, P.A. 2000
Solitary waves in nonlinear beam equations;
stability, fission and fusion.
Nonlinear Dynamics 21 31-53.
Abstract & preprint;
- [40] Champneys, A.R. and Fraser, W.B. 2000 The `Indian rope trick'
for a parametrically excited flexible rod: I linearised analysis.
Proc. Roy. Soc. Lond. A 456 553-570.
Abstract & preprint;
- [41] A.R. Champneys & Y.S. Kivshar. 2000
Origin of Multikinks in Nonlinear Dispersive Systems
Phys. Rev. E 61 2551-2554.
Abstract & preprint
- [42] Champneys, A.R., Groves, M.D. and Woods, P.D. 2000
A global characterization of gap solitary-wave solutions
to a coupled KdV system. Phys. Lett. A , 271 ,
178-190.
Abstract & preprint
- [43] Kolossovski, K.,
Buryak, A.V., Steblina, V.V, Champneys, A.R. and Sammut, R.A.
2000 Higher-order nonlinear modes and bifurcation phenomena due to
degenerate parameteric four-wave mixing. Phys. Rev. E
62 4309-4317
Abstract & preprint
- [44] Champneys, A.R. & Haerterich, J. 2000 Cascades of
homoclinics orbits to a saddle-centre for reversible and
perturbed Hamiltonian systems.
Dynamics and Stability of System 15 231-252.
Abstract & preprint
- [45] Oldeman, B.E., Krauskopf, B. and Champneys, A.R.
Death of period-doublings: locating the homoclinic-doubling cascade.
Physica D 146 100-120.
Abstract & preprint
- [46] Champneys, A.R. 2000
Codimension-one persistence beyond all
orders of homoclinic orbits to singular saddle centres in
reversible systems. Nonlinearity 14
87-112.
Abstract & preprint
- [47] Stump, D.M., Champneys A.R. and van der Heijden G.H.M.
The torsional buckling and writhing of a simply-supported
rod hanging under gravity.
International Journal of Solids and Structures
38 795-813.
Abstract & preprint
- [48] di Bernardo, M., Budd, C.J. and Champneys, A.R. 2001
Grazing and Border--Collision in Piecewise-smooth Systems:
A Unified Analytical Framework. Phys. Rev. Lett.
86 2553-2556
Abstract & preprint
- [49] Champneys, A.R., Malomed, B.A., Yang, J. and Kaup, D.J. 2001
"Embedded solitons": solitary waves in resonance with the linear spectrum.
Physica D , 152 340-354.
Abstract & preprint
- [50] Yang, J., Malomed, B.A., Kaup, D.J. and Champneys, A.R. 2001
Embedded solitons: a new type of solitary wave.
Mathematics & Computer Simulation 56 , 585-600
- [51] Oldeman, B.E., Krauskopf, B., and Champneys, A.R. 2001
Numerical unfoldings of resonant homoclinic flip bifurcations.
Nonlinearity 14 597-621.
Abstract & preprint
- [52] di Bernardo, M., Budd C.J. and Champneys, A.R 2001
Corner collision implies border-collision bifurcation.
dynamical systems. Physica D 154 171-194.
Abstract & preprint
- [53] di Bernardo, M., Budd, C.J. and Champneys, A.R. 2001
Unified derivation of normal forms maps for grazing
bifurcations in N-dimensional piecewise-smooth dynamical systems
Physica D 160 222-254.
- [54] Skryabin, D.V. and Champneys, A.R. 2001 Walking
Cavity Solitons. Phys.\ Rev.\ E
6306 art. no. 066610.
Abstract & preprint
- [56] Champneys, A.R., Vanden-Broek J.-M. and Lord, G.J. 2002
Do true elevation solitary waves exist? A numerical investigation.
J.Fluid Mech. 454 403-417.
Abstract & preprint
- [57] Roberts, I. Jones, D.P., Lieven, N.A.J., di Bernardo, M.
and Champneys, A.R. 2002
Analysis of piecewise linear aeroelastic systems using numerical continuation.
Proc. Inst. Mech. Eng. G: J. Aero. Eng. 216 1-12.
Abstract & preprint
Journal publications to appear
- [58] Fraser, W.B. and Champneys A.R. The `Indian rope trick' for
a parametrically excited flexibel rod; nonlinear and subharminic
analysis. To appear in Proc. Roy. Soc. Lond. A
Abstract & preprint
- [59] van der Hiejden, G.H.M., Champneys, A.R. and Thompson, J.M.T.
Spatially complex localisation in twisted elastic rods
constrined to lie on a cylinder.
To appear in Int. J. Solids & Strutures
Abstract & preprint
- [60] Kolossovski, K., Champneys, A.R., Buryak A.V. and Sammut, R.A.
Multipulse embedded solitons as bound states of quasi-solitons. To appear in
Physica D .
Abstract & preprint
Submitted papers
- [61] Mullin, T. Champneys, A.R. Fraser, W.B., Galan, J. and Acheson, D.
The `Indian rod trick' via parametric excitation. Submitted to
Proc. Roy. Soc. Lond. A
Abstract & preprint
- [62] Homer, M. Champneys, A., Hunt, G. and Cooper, N.
Mathematical modeling of the radial profile of basilar membrane
vibrations in the inner ear. Submitted.
Abstract & preprint
- [63] Champneys, A.R. and Yang, Jianke
A scalar nonlocal bifurcation of solitary waves for coupled nonlinear
Schrodinger systems. Submitted to Nonlinearity .
- [64] Wagenknecht, T. and Champneys, A.R.
When gap solitons become embedded solitons; an unfolding via Lin's method.
Submitted.
Abstract & preprint
Refereed conference proceedings articles
- [C1] van der Heijden, G.H.M., Champneys, A.R. & Thompson,
J.M.T. 1996 Homoclinic bifurcation and localised torsional buckling of
elastic rods. Proceedings IUTAM meeting on the Interaction
between Dynamics and Control , Eindhoven, April 1996.
- [C2] di Bernardo, M., Champneys A.R., Garofalo, F., Gilelmo, L. &
Vasca, F. 1996 Nonlinear phenomena in the DC/DC buck converter.
Proceedings NDES , Seville, June 1996.
- [C3] Lord, G.J., Champneys A.R. & Hunt, G.W. 1997 The role of
homoclinic orbits in explaining the buckling of long thin cylindrical
shells. IUTAM symposium on Applications of Nonlinear and
Chaotic Dynamics in Mechanics , Cornell University, July 1997.
Abstract & preprint;
- [C4] Thompson, J.M.T., van der Heijden, G.H.M. & Champneys, A.R. 1998
Twisting, writhing and buckling of pipelines. 21st Annual Offshore
Pipeline Technology Conference , Oslo, February 1998.
- [C5] di Bernardo, M., Champneys, A.R., Budd, C.J. and Vasca, F. 1999
Sliding orbits and double spiral bifurcation diagrams in power electronic
DC/DC converters. IEEE International Symposium on Circuits
and Systems, May 1999 Orlando USA. V-262.
- [C6] Krauskopf, B., Oldeman, B.E. and Champneys, A.R. 1999
Resonant homoclinic flip bifurcations: a numerical investigation
Equidiff Berlin.
ANM Research Report 13.99
- [C7] Champneys, A.R. and Malomed, B.A. 1999
A new class of optical solitary waves: embedded solitons.
Nonlinear Guided Waves and
Their Applications Dijon, September 1-3 1999.
- [C8] Skryabin, D.V., Firth W.J. and Champneys 2000 Frequency selection
by soliton exciation in nondegenerate intracavity downconversion
CLEO/QELS 2000 San Fransisco May 2000.
Other
- [O1] Champneys, A.R. & Hjorth, P.G. 1993 Integration of
separatrix-crossing orbits. Technical Report
Mathematical Institute, Technical University of Denmark
- [O2] Champneys, A.R., Kuznetsov, Yu.A. & Sandstede, B.
1995 HomCont: An auto86 driver for homoclinic bifurcation analysis.
Version 2.0. CWI Report AM-R9516 , CWI Amsterdam.
- [O3] Doedel, E.J. with Champneys, A.R., Fairgrieve, T.F.,
Kuznetsov, {Yu}.A., Sandstede, B. & Wang, X. 1997 AUTO97
Continuation and bifurcation
software for ordinary differential equations.
Available by anonymous ftp from
ftp.cs.concordia.ca directory pub/doedel/auto
- [O4] Champneys, A.R., Hunt G.W. & Thompson J.M.T. (Eds.)
1997 Localization and solitary waves in solid mechanics
Special Issue Phil.\ Trans.\ Roy.\ Soc.\ Lond.
355 , 2077-2213.
- [O5] Champneys, A.R. 1999
`Size Matters' Nonesuch (The University of Bristol Magazine)
Autumn 1999 p.60.
- [O6] Beyn, W.J., Champneys, A.R., Doedel, E.J., Goverts, W.,
Kuznetsov, Yu.A. and Sandstede, B. 2002.
Numerical continuation and computation of normal forms.
Chapter 4 (pp. 149-220) of ` Handbook of Dynamical Systems III:
towards applications ', Editor: Fiedler, B. Elsevier.
Draft available
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