Chris Eilbeck - Index page

Professor J C Eilbeck, FRSE - Home Page

Chris Eilbeck has been at Heriot-Watt 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 post-doctoral year at ICTP, Trieste, followed by a spell as a RA in the Department of Mathematics, UMIST. He was Head of Department at Heriot-Watt for the period 1984-89, and Dean of the Faculty of Science 1998-2001. He was visiting fellow at Corpus Christi College, Cambridge, Oct-Dec. 2001, and at the Mittag-Leffler Institute, Stockholm, Nov-Dec 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 soliton-related problems in mathematical physics. One lattice equation which he has worked on a lot is the Discrete Self-Trapping equation, a generalized discrete Nonlinear Schrödinger equation. Recently he has worked with Russell, Marín and Cruzeiro-Hansson in studies of localised lattice modes and applications to HT_c.

In addition he works on the corresponding quantum problems. He has a long-running interest in numerical and analytic studies of reaction-diffusion 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 meetings are shown here.

He is a keen mountaineer and likes listening to modern jazz.

Recent Conferences

He organised a Workshop on Environmental Modelling in March 2001 and a Workshop on Mathematical Modelling in Science and Engineering in May 2001. He was one of the organisers for the Meeting on Integrable Systems at the Newton Institute, July-December 2001, and for the Mini-Programme on the Algebraic Theory of Differential Equations, Heriot-Watt University, Edinburgh, 31 July to 11 August 2006

Teaching:

I'm currently teaching Optimization, F14ZU1 and Numerical Methods for PDEs, F14ZH2. The latter is also part of the our MSc in Financial Mathematics.

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).

Some recent papers:

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. Aharonov-Bohm 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 15.1-15.31. 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, cond-mat/0612066, Europhysics Letters 78, 10004 (2007), doi: 10.1209/0295-5075/78/10004 .
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 (DCDS-A), 21, 445-475, 2008.
Addition formulae over the Jacobian pre-image 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, 37-48, 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., 58 450-467 (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, 69-85, 2008.
Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type: J. C. Eilbeck, S. Matsutani, and Y. Ônishi, arXiv link, submitted for publication, 2008.
Interaction of moving discrete breathers with simulated interstitial defects: J. Cuevas, B. Sanchez-Rey, J. C. Eilbeck, and F. M. Russell, PDF copy, submitted for publication, 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.
Persistent mobile lattice excitations in a crystalline insulator: F. M. Russell and J. C. Eilbeck, PDF copy , to appear in DCDS-S (2011).
Breathers and kinks in a simulated crystal experiment: Q. Dou, J. Cuevas, J. C. Eilbeck, and F. M. Russell, arXiv link, to appear in DCDS-S (2011).
Sigma, tau and Abelian functions of algebraic curves: J. C. Eilbeck, V. Z. Enolski, and J. Gibbons, arXiv link, submitted for publication, 2010.
Abelian functions associated with genus three algebraic curves: J. C. Eilbeck, M. England and Y. Onishi, arXiv link, submitted for publication, 2010.

A full publication list is available.

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Chris Eilbeck / Heriot-Watt University /J.C.Eilbeck at hw.ac.uk / tel. +44 (0)131 451 3220