Publications of Alan Champneys 1991-2002

• Books
• Journal publications
• Journal publications to appear
• Submitted papers
• Conference contributions
• Other

Books

• [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.

Journal publications

• [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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