Professor J C Eilbeck, FRSE  Home Page
Chris Eilbeck has been at HeriotWatt since 1973, except for the year
1983/84, which he spent at the Center for Nonlinear Studies, Los
Alamos National Laboratory, New Mexico. Prior to coming to Edinburgh,
he took his undergraduate degree (BA in Theoretical Physics) at The
Queen's College, Oxford, and his PhD in the Department of Physics,
University of Lancaster. He spent a postdoctoral year at ICTP,
Trieste, followed by a spell as a RA in the Department of Mathematics,
UMIST. He was Head of Department at HeriotWatt for the period
198489, and Dean of the Faculty of Science 19982001. He was
visiting fellow at Corpus Christi College, Cambridge, OctDec. 2001,
and at the MittagLeffler Institute, Stockholm, NovDec 2005.
His current research interests are in the study
of solitons, both in
the numerical study of solitons on lattices, and the use of computer
algebra to study exact periodic and quasiperiodic solutions of soliton
and solitonrelated problems in mathematical physics. One lattice
equation which he has worked on a lot is the Discrete
SelfTrapping equation, a generalized discrete Nonlinear
Schrödinger equation. Recently he has worked with Russell,
Marín and CruzeiroHansson in studies of
localised lattice modes and applications to HT_{c}.
In addition he works on the corresponding quantum problems. He
has a longrunning interest in numerical and analytic studies of
reactiondiffusion systems, travelling waves
and pattern formation in physiology, embryology and ecology.
His most recent work is in the theory of Weierstrass functions for
curves of higher genus, see
the Weierstrass web
page which is under construction. This work has even lead to some
new results in the genus 1 case.
Some photographs taken at various ICMS and other meetings are
shown here.
He is a keen mountaineer and likes listening to modern jazz.
Books:
 Solitons and Nonlinear Wave Equations, R K Dodd, J C
Eilbeck, J D Gibbon, and H C Morris,
 pp 640, London: Academic
Press (1982, reprinted 1984). Russian edition: Mir Press, Moscow
(1988).
Rock Climbing in the Lake District A.G. Cram,
J. C. Eilbeck, W. Birkett, Constable, (1987).
Films:
Some 16mm computerproduced cine
films made in the '70s and '80s.
Some of my older papers published in obscure conference proceedings
which are now difficult to obtain.
Some recent papers:
(> publications 20002002 )
(> publications 20032004 )
(> publications 20052006 )
 Abelian Functions for Trigonal Curves of Genus Three

J. C. Eilbeck, V. Z. Enolski, S. Matsutani, Y. Ônishi, and
E. Previato, International Mathematics Research Notices,
2007, Art.ID: rnm140 (38 pages), 2007, Abstract,
PDF Copy.
 Localization and Transport of Charge by Nonlinearity and
Spatial Discreteness in Biomolecules and Semiconductor
Nanorings. AharonovBohm effect for neutral excitons.
 F. Palmero, J. Cuevas, F.R. Romero, J.C. Eilbeck,
R.A. Römer, and J. Dorignac. In S.E. Lyshevski, Ed.,
Handbook on Nano and Molecular Electronics, pages 15.115.31. CRC
Press (Taylor and Francis Group, Florida), ISBN: 0849385288, 2007.
 Evidence for moving breathers in a layered crystal insulator
at 300K.
 F. M. Russell and J. C. Eilbeck, condmat/0612066,
Europhysics Letters 78, 10004 (2007), doi:
10.1209/02955075/78/10004 .
 Spectral Curves of Operators with Elliptic Coefficients
 J.C. Eilbeck, V.Z. Enolski, and E. Previato, SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications),
3, 045, 2007.
 Thresholds for breather solutions of the Discrete Nonlinear
Schrödinger Equation with saturable and power
nonlinearity
 J. Cuevas, J. C. Eilbeck, and N. I. Karachalios, nlin.PS/0609023,
Discrete and Continuous Dynamical Systems  Series A (DCDSA),
21, 445475, 2008.
 Addition formulae over the Jacobian preimage of
hyperelliptic Wirtinger varieties

J.C. Eilbeck, V.Z. Enol'skii, S. Matustani, Y. Ônishi, and
E. Previato,
PDF copy, Journal für die reine und
angewandte Mathematik (Crelle's Journal), 619, 3748, 2008.
 Abelian Functions for Purely Trigonal Curves of Genus
four
 S. Baldwin, J. C. Eilbeck, J. Gibbons, and
Y. Ônishi, math.AG/0612654,
J. Geom. Phys., 58 450467 (2008). DOI:
10.1016/j.geomphys.2007.12.001
 A lower bound for the power of periodic solutions of the
defocusing Discrete Nonlinear Schrödinger equation

J. Cuevas, J. C. Eilbeck, and N.I. Karachalios, PDF Copy, Dynamics of
Partial Differential Equations, 5, 6985, 2008.
 Abelian functions associated with a cyclic tetragonal curve of
genus six
 M. England and J. C. Eilbeck, arXiv link, J. Phys. A:
Math. Theor. 42, (2009) 095210.
 Sigma, tau and Abelian functions of algebraic curves
 J. C. Eilbeck, V. Z. Enolski, and J. Gibbons, arXiv link,
J. Phys. A: Math. Theor. 43 (2010) 455216
 Some addition formulae for Abelian functions for elliptic and
hyperelliptic curves of cyclotomic type
 J. C. Eilbeck, S. Matsutani, and Y. Ônishi, arXiv link,
Phil. Trans. Roy. Soc. A., 369, 12451263 (2011).
 Interaction of moving discrete breathers with interstitial
defects
 J. Cuevas, B. SanchezRey, J. C. Eilbeck, and
F. M. Russell,
PDF copy, Discrete and Continuous Dynamical Systems  Series
S, 4 1057  1067 (2011).
 Persistent mobile lattice excitations in a crystalline
insulator
 F. M. Russell and J. C. Eilbeck,
PDF copy, Discrete and Continuous Dynamical Systems  Series
S, 4 12671285 (2011).
 Breathers and kinks in a simulated crystal experiment
 Q. Dou, J. Cuevas, J. C. Eilbeck, and F. M. Russell,
PDF copy, Discrete and Continuous Dynamical Systems 
Series S, 4 11071118 (2011).
 Abelian functions associated with genus three algebraic curves
 J. C. Eilbeck, M. England and Y. Ônishi, LMS Journal of
Computation and Mathematics, 14, 291326 (2011).
 Some new addition formulae for Weierstrass elliptic
functions
 J. C. Eilbeck, M. England and
Y. Ônishi, arXiv version, Proc. Roy. Soc. A, 470 20140051 (14 pages), 2014.
 Periods of second kind differentials of (n,s)curves
 J. C. Eilbeck, K. Eilers and V. Z. Enolski arXiv version, arXiv 1305.3201
(2013), published in Trudy Moskovskogo Matematicheskogo
Obshchestva (Proceedings of Moscow Mathematical Society), v.74, N2,
2013, p. 297315.
 Quantization of βFermiPastaUlam Lattice with Nearest
and Nextnearest Neighbour Interactions
 Aniruddha Kibey, Rupali Sonone, Bishwajyoti Dey, J. Chris Eilbeck
arXiv 1408.0212,
Physica D, 294, 4353, 2015.
 Numerical simulations of nonlinear modes in mica:
past, present and future
 J. Bajars, J. C. Eilbeck and B. Leimkuhler,
ArXiv 1408.6853
in Quodons in Mica, Springer Series in
Materials Science, 221, Eds. Archilla, J. F. R., Jiménez,
N., SánchezMorcillo, V. J., GarcíaRaffi, L. M., 3567, 2015.
 Nonlinear propagating localized modes in a 2D hexagonal
crystal lattice
 J. Bajars, J. C. Eilbeck and B. Leimkuhler,
ArXiv 1409.0355, Physica D, 301–302, 820 (2015).
 Recursion Relations on the Power Series Expansion of the
Universal Weierstrass Sigma Function
 J. Bajars, J. C. Eilbeck and B. Leimkuhler,
ArXiv 1409.0355, Physica D, 301–302, 820 (2015).
 Recursion Relations on the Power Series Expansion of the
Universal Weierstrass Sigma Function
 J. Chris Eilbeck and Y. Ônishi, in RIMS Kôkyûroku Bessatsu
B78:
Mathematical structures of integrable systems and their applications,
ed. Shinsuke Iwao, pp 7798. (2020)
 2D mobile breather scattering in a hexagonal crystal lattice
 J. Bajars, J. C. Eilbeck and B. Leimkuhler,
ArXiv 2007.12079 (2020),
Phys. Rev. E 103, 022212 (2021)
 Statistical Evidence for a Helical Nascent Chain
 Leonor Cruzeiro, Andrew C. Gill and J. Chris Eilbeck,
Biomolecules (2021), 11, 357.
 Exact analytic multiquanta states of the Davydov Dimer
 C. Athorne, L. Cruzeiro and J. C. Eilbeck, arXiv:2205.12016 (2022)
A full publication list is available.
> Mathematics Home page
Chris Eilbeck / HeriotWatt University /J.C.Eilbeck at
hw.ac.uk / tel. +44 (0)131 451 3220