School of Mathematics, Statistics & Actuarial Science

About

Andy believes in inspiring the next generation of mathematicians, and is involved with School Outreach activities with local schools and the general public. Until late 2014 he was Head of the Mathematics group but has now commenced a five-year EPSRC Established Career Fellowship (2015-2020), working on the project Cluster algebras with periodicity and discrete dynamics over finite fields. 

Contact Information

Address

Room 265

Due to study leave Andy is not able to offer any office hours during autumn 2017

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Publications

Also view these in the Kent Academic Repository

Article
Hone, A., Kouloukas, T. and Ward, C. (2017). On reductions of the Hirota-Miwa equation. Symmetries, Integrability and Geometry: Methods and Applications [Online] 13:1-17. Available at: https://dx.doi.org/10.3842/SIGMA.2017.057.
Hone, A., Novikov, V. and Wang, J. (2017). Two-component generalizations of the Camassa-Holm equation. Nonlinearity [Online] 30:622-658. Available at: http://iopscience.iop.org/article/10.1088/1361-6544/aa5490/meta;jsessionid=0AADAAD96C412EF897587E993641D098.c2.iopscience.cld.iop.org.
Hone, A., Novikov, V. and Wang, J. (2016). Generalizations of the short pulse equation. ArXiv [Online]. Available at: https://arxiv.org/abs/1612.02481.
Hone, A. (2016). On the continued fraction expansion of certain Engel series. Journal of Number Theory [Online] 164:269-281. Available at: http://dx.doi.org/10.1016/j.jnt.2015.12.024.
Fedorov, Y. and Hone, A. (2016). Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties. Journal of Integrable Systems [Online] 1. Available at: https://doi.org/10.1093/integr/xyw012.
Hone, A. (2015). Continued fractions for some transcendental numbers. Monatshefte fur Mathematik [Online]. Available at: http://link.springer.com/article/10.1007/s00605-015-0844-2?wt_mc=internal.event.1.SEM.ArticleAuthorOnlineFirst.
Hone, A. (2015). Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers. Journal of Integer Sequences [Online] 18:1-10. Available at: https://cs.uwaterloo.ca/journals/JIS/VOL18/Hone/hone3.pdf.
Hone, A. and Towler, K. (2015). Non-standard discretization of biological models. Natural Computing [Online] 14:39-48. Available at: http://link.springer.com/article/10.1007%2Fs11047-014-9463-4#page-1.
Hone, A. (2015). Algebraic entropy for algebraic maps. Journal of Physics A: Mathematical and Theoretical [Online] 49. Available at: http://dx.doi.org/10.1088/1751-8113/49/2/02LT01.
Hone, A. and Lafortune, S. (2014). Stability of stationary solutions for nonintegrable peakon equations. Physica D: Nonlinear Phenomena [Online] 269:28-36. Available at: http://dx.doi.org/10.1016/j.physd.2013.11.006.
Hone, A. and Inoue, R. (2014). Discrete Painlevé equations from Y-systems. Journal of Physics A: Mathematical and Theoretical [Online] 47. Available at: http://iopscience.iop.org/article/10.1088/1751-8113/47/47/474007/meta;jsessionid=1BAB92959D74F9C50E2861EC9E77E502.c1.
Hone, A. and Ward, C. (2014). A family of linearizable recurrences with the Laurent property. Bulletin of the London Mathematical Society [Online] 46:503-516. Available at: http://dx.doi.org/10.1112/blms/bdu004.
Fordy, A. and Hone, A. (2014). Discrete integrable systems and Poisson algebras from cluster maps. Communications in Mathematical Physics [Online] 325:527-584. Available at: http://dx.doi.org/10.1007/s00220-013-1867-y.
Hone, A. et al. (2013). Integrability of reductions of the discrete Korteweg-de Vries and potential Korteweg-de Vries equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences [Online] 469. Available at: http://dx.doi.org/10.1098/rspa.2012.0747.
Hone, A., Ragnisco, O. and Zullo, F. (2013). Properties of the series solution for Painlevé I. Journal of Nonlinear Mathematical Physics [Online] 20:85-100. Available at: http://dx.doi.org/10.1080/14029251.2013.862436.
Fordy, A. and Hone, A. (2011). Symplectic Maps from Cluster Algebras. Symmetry, Integrability and Geometry: Methods and Applications [Online] 7:1-12. Available at: http://dx.doi.org/10.3842/SIGMA.2011.091.
Chu, D., Zabet, N. and Hone, A. (2011). Optimal Parameter Settings for Information Processing in Gene Regulatory Networks. BioSystems [Online]:182-196. Available at: http://www.cs.kent.ac.uk/pubs/2011/3081.
Hone, A. and Petrera, M. (2009). Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras . Journal of Geometric Mechanics [Online] 1 :55-85. Available at: http://dx.doi.org/10.3934/jgm.2009.1.55.
Hone, A., Lundmark, H. and Szmigielski, J. (2009). Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa--Holm type equation. Dynamics of Partial Differential Equations [Online] 6 :253-289. Available at: http://www.intlpress.com/DPDE/journal/DPDE-v06.php.
Hone, A. and Swart, C. (2008). Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences. Mathematical Proceedings of the Cambridge Philosophical Society [Online] 145:65-85. Available at: http://dx.doi.org/10.1017/s030500410800114x.
Hone, A., Novikov, V. and Verhoeven, C. (2008). An extended Henon-Heiles system. Physics Letters A [Online] 372:1440-1444. Available at: http://dx.doi.org/10.1016/j.physleta.2007.09.063.
Common, A. and Hone, A. (2008). Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation. Journal of Physics A: Mathematical and Theoretical [Online] 41:485203. Available at: http://dx.doi.org/10.1088/1751-8113/41/48/485203.
Hone, A. and Wang, J. (2008). Integrable peakon equations with cubic nonlinearity. Journal of Physics A: Mathematical and Theoretical [Online] 41. Available at: http://dx.doi.org/10.1088/1751-8113/41/37/372002 .
Timmis, J. et al. (2008). Theoretical advances in artificial immune systems. Theoretical Computer Science [Online] 403:11-32. Available at: http://dx.doi.org/10.1016/j.tcs.2008.02.011.
Hone, A. (2007). Sigma function solution of the initial value problem for Somos 5 sequences. Transactions of the American Mathematical Society [Online] 359:5019-5034. Available at: http://dx.doi.org/10.1090/S0002-9947-07-04215-8.
Hone, A. (2007). Laurent Polynomials and Superintegrable Maps. Symmetry, Integrability and Geometry: Methods and Applications [Online] 3:1-18. Available at: http://www.emis.de/journals/SIGMA/2007/022/.
Hone, A. (2007). Singularity confinement for maps with the Laurent property. Physics Letters A [Online] 361:341 -345. Available at: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-4M27S0J-3&_user=125871&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000010239&_version=1&_urlVersion=0&_userid=125871&md5=03ddab063508d4dd3af4ab7ba9c8bdf1.
Sen, A., Hone, A. and Clarkson, P. (2006). On the Lax pairs of symmetric Painleve equations. Studies in Applied Mathematics [Online] 117:299-319. Available at: http://dx.doi.org/10.1111/j.1467-9590.2006.00356.x.
Hone, A. (2006). Diophantine non-integrability of a third order recurrence with the Laurent property. Journal of Physics A: Mathematical and General [Online] 39:L171-L177. Available at: http://dx.doi.org/10.1088/0305-4470/39/12/L01.
Braden, H., Enolskii, V. and Hone, A. (2005). Bilinear recurrences and addition formulae for hyperelliptic sigma functions. Journal of Nonlinear Mathematical Physics [Online] 12:46-62. Available at: http://dx.doi.org/10.2991/jnmp.2005.12.s2.5.
Hone, A. (2005). Elliptic curves and quadratic recurrence sequences. Bulletin of the London Mathematical Society [Online] 37:161-171. Available at: http://dx.doi.org/10.1112/S0024609304004163 .
Holm, D. and Hone, A. (2005). A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith). Journal of Nonlinear Mathematical Physics [Online] 12:380-394. Available at: http://staff.www.ltu.se/~norbert/home_journal/electronic/v12s1.html.
Sen, A., Hone, A. and Clarkson, P. (2005). Darboux transformations and the symmetric fourth Painlevé equation. Journal of Physics A: Mathematical and General [Online] 38:9751-9764. Available at: http://dx.doi.org/10.1088/0305-4470/38/45/003.
Hone, A. (2005). Non-existence of elliptic travelling wave solutions of the complex Ginzburg-Landau equation. Physica D: Nonlinear Phenomena [Online] 205:292-306. Available at: http://dx.doi.org/10.1016/j.physd.2004.10.011 .
Hone, A. and Novikov, V. (2004). On a functional equation related to the intermediate long wave equation . Journal of Physics A: Mathematical and General [Online] 37:L399-L406. Available at: http://dx.doi.org/10.1088/0305-4470/37/32/L02.
Hone, A. and Wang, J. (2003). Prolongation algebras and Hamiltonian operators for peakon equations. Inverse Problems [Online] 19:129-145. Available at: http://dx.doi.org/10.1088/0266-5611/19/1/307.
Clarkson, P., Hone, A. and Joshi, N. (2003). Hierarchies of Difference Equations and Bäcklund Transformations. Journal of Nonlinear Mathematical Physics [Online] 10:13-26. Available at: http://dx.doi.org/10.2991/jnmp.2003.10.s2.2.
Holm, D. and Hone, A. (2003). On the non-integrability of a fifth order equation with integrable two-body dynamics. Theoretical and Mathematical Physics [Online] 137:1459-1471. Available at: http://dx.doi.org/10.1023/A:1026060924520.
Degasperis, A., Holm, D. and Hone, A. (2002). A new integrable equation with peakon solutions. Theoretical and Mathematical Physics [Online] 133:1463-1474. Available at: http://dx.doi.org/10.1023/A:1021186408422.
Hone, A. (2002). Lattice equations and tau-functions for a coupled Painlevé system. Nonlinearity [Online] 15:735-745. Available at: http://dx.doi.org/10.1088/0951-7715/15/3/313.
Hone, A., Kuznetsov, V. and Ragnisco, O. (2001). Backlund transformations for the sl(2) Gaudin magnet. Journal of Physics A: Mathematical and General [Online] 34:2477-2490. Available at: http://iopscience.iop.org/0305-4470/34/11/336;jsessionid=9D62B776C809D1BCE6AEDFD01F52CDB3.c1.
Nijhoff, F., Hone, A. and Joshi, N. (2000). On a Schwarzian PDE associated with the KdV Hierarchy. Physics Letters A [Online] 267:147-156. Available at: http://dx.doi.org/10.1016/S0375-9601(00)00063-3.
Nijhoff, F., Joshi, N. and Hone, A. (2000). On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation. Physics Letters A [Online] 264:396-406. Available at: http://dx.doi.org/10.1016/S0375-9601(99)00764-1.
Hone, A., Kuznetsov, V. and Ragnisco, O. (1999). Backlund transformations for many-body systems related to KdV. Journal of Physics A: Mathematical and General [Online] 32:L299-L306. Available at: http://dx.doi.org/10.1088/0305-4470/32/27/102.
Book section
Hone, A. and Krusch, S. (2017). Differential Geometry and Mathematical Physics. in: Analysis and Mathematical Physics. World Scientific, pp. 1-40. Available at: http://www.worldscientific.com/worldscibooks/10.1142/Q0029.
Conference or workshop item
Zabet, N., Hone, A. and Chu, D. (2010). Design Principles of Transcriptional Logic Circuits. in: Artificial Life XII Proceedings of the Twelfth International Conference on the Synthesis and Simulation of Living Systems. MIT Press, pp. 182-196. Available at: http://www.cs.kent.ac.uk/pubs/2010/3036.
Hone, A. and Irle, M. (2009). On the non-integrability of the Popowicz peakon system. in: 7th AIMS conference on Dynamical Systems, Differential Equations and Applications. AIMS, pp. 359-366. Available at: http://www.aimsciences.org/journals/contentsListPro.jsp?pubID=262.
Hone, A. (2008). Algebraic curves, integer sequences and a discrete Painleve transcendent. in: SIDE 6.. Available at: http://arxiv.org/abs/0807.2538.
Kelsey, J., Timmis, J. and Hone, A. (2003). Chasing Chaos. in: Sarker, R. A. et al. eds. Proceedings of the Congress on Evolutionary Computation (CEC). Canberra. Australia: IEEE, pp. 413-419. Available at: http://www.cs.kent.ac.uk/pubs/2003/1758.
Total publications in KAR: 49 [See all in KAR]
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Research Interests

  • Discrete and continuous integrable systems
  • Cluster algebras
  • Dynamics over finite fields
  • Coherent structures in PDEs
  • Painlevé equations
  • Solvable models in physics and biology.
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Research Supervisees

  • Lucy Barnes - Nonlinear differential equations, modelling biological systems and topological solitons.
  • Joe Pallister - Cluster algebras and discrete integrable systems
  • Nitin Serwa - Symbolic computation and integrable systems

 

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School of Mathematics, Statistics and Actuarial Science (SMSAS), Sibson Building, Parkwood Road, Canterbury, CT2 7FS

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Last Updated: 02/10/2017