Professor John Chris Eilbeck
Heriot-Watt University
Emeritus, Mathematics
United Kingdom
My co-authors include
Dr Leonor Cruzeiro
Andrey Tsiganov
My Publications
Quantization of <mml:math altimg="si42.gif" display="inline" overflow="scroll" xmlns:xo...
Physica D Nonlinear Phenomena
February 2015
Some new addition formulae for Weierstrass elliptic functions
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
September 2014
Periods of second kind differentials of $(n,s)$-curves
Transactions of the Moscow Mathematical Society
April 2014
Abelian functions associated with genus three algebraic curves
LMS Journal of Computation and Mathematics
November 2011
Addition formulae for Abelian functions associated with specialized curves
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering...
February 2011
Persistent mobile lattice excitations in a crystalline insulator
Discrete and Continuous Dynamical Systems - S
December 2010
Interaction of moving discrete breathers with interstitial defects
Discrete and Continuous Dynamical Systems - S
December 2010
Breathers and kinks in a simulated crystal experiment
Discrete and Continuous Dynamical Systems - S
December 2010
Sigma, tau and Abelian functions of algebraic curves
Journal of Physics A Mathematical and Theoretical
October 2010
Abelian Functions for Trigonal Curves of Genus Three
International Mathematics Research Notices
July 2010
Abelian functions associated with a cyclic tetragonal curve of genus six
Journal of Physics A Mathematical and Theoretical
February 2009
Abelian functions for cyclic trigonal curves of genus 4
Journal of Geometry and Physics
April 2008
Thresholds for breather solutions of the discrete nonlinear Schrödinger equation with s...
Discrete and Continuous Dynamical Systems
March 2008
Addition formulae over the Jacobian pre-image of hyperelliptic Wirtinger varieties
Journal für die reine und angewandte Mathematik (Crelles Journal)
January 2008
A lower bound for the power of periodic solutions of the defocusing discrete nonlinear ...
Dynamics of Partial Differential Equations
January 2008
Evidence for moving breathers in a layered crystal insulator at 300 K
EPL (Europhysics Letters)
March 2007
Spectral Curves of Operators with Elliptic Coefficients
Symmetry Integrability and Geometry Methods and Applications
March 2007
Discrete soliton collisions in a waveguide array with saturable nonlinearity
Physics Letters A
October 2006
Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice
Physica D Nonlinear Phenomena
September 2006
Aharonov-Bohm effect for an exciton in a finite-width nanoring
Physical Review B
August 2005
Dynamical two electron states in a Hubbard-Davydov model
The European Physical Journal B
November 2004
Trapping in quantum chains
Physics Letters A
October 2004
Quantum Signatures of Breather-Breather Interactions
Physical Review Letters
July 2004
Covariant genus 2 hyperelliptic functions
Mathematical Proceedings of the Cambridge Philosophical Society
March 2004
Identities for the classical genus two function
Journal of Geometry and Physics
November 2003
Influence of moving breathers on vacancies migration
Physics Letters A
September 2003
The hyperelliptic -function and the integrable massive Thirring model
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
July 2003
SOME EXACT RESULTS FOR QUANTUM LATTICE PROBLEMS
May 2003
THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION — 20 YEARS ON
May 2003
Multidimensional Schrödinger equations with Abelian potentials
Journal of Mathematical Physics
June 2002
Varieties of elliptic solitons
Journal of Physics A General Physics
March 2001
Breathers in cuprate-like lattices
Physics Letters A
March 2001
Exact energy bands and Fermi surfaces of separable Abelian potentials
Journal of Physics A General Physics
January 2001
Analytical approach to the Davydov-Scott theory with on-site potential
January 2001
Ephaptic coupling of myelinated nerve fibers
Physica D Nonlinear Phenomena
January 2001
Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations
Journal of Mathematical Physics
December 2000
Quasi-periodic and periodic solutions for coupled nonlinear Schrodinger equations of Ma...
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
September 2000
Breathers in systems with intrinsic and extrinsic nonlinearities
Physica D Nonlinear Phenomena
August 2000
Moving kinks and nanopterons in the nonlinear Klein–Gordon lattice
Physica D Nonlinear Phenomena
April 2000
Interplay between dispersive and non-dispersive modes in the polaron problem
Physics Letters A
February 2000
Bilinear operators and the power series for the Weierstrass sigma function
Journal of Physics A General Physics
January 2000
A breather-like localized mode in a Fermi-Pasta-Ulam lattice interacting with an electron
Journal of Physics Condensed Matter
June 1998
Bound states of lattice solitons and their bifurcations
Physica D Nonlinear Phenomena
September 1997
On the Periodic Lotka–Volterra Competition Model
Journal of Mathematical Analysis and Applications
June 1997
Moving breathers in a chain of magnetic pendulums
March 1997
Some applications of computer algebra to problems in theoretical physics
Mathematics and Computers in Simulation
April 1996
Quasi-Periodic Solutions of the Coupled Nonlinear Schrodinger Equations
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
December 1995
Stationary states in a doubly nonlinear trimer model of optical couplers
Physica Scripta
October 1995
Mathematical modelling of weakly nonlinear pulses in a retinal neuron
Chaos Solitons & Fractals
March 1995
On the two-gap locus for the elliptic Calogero-Moser model
Journal of Physics A General Physics
February 1995
Conditions under which Na+channels can Boost conduction of small graded potentials
Journal of Theoretical Biology
February 1995
Analysis of bifurcations in reaction–diffusion systems with no-flux boundary conditions...
Proceedings of the Royal Society of Edinburgh Section A Mathematics
January 1995
Quantum lattice solitons
Physica D Nonlinear Phenomena
November 1994
General method to solve Hamiltonians with infinite-range interactions
Physical Review A
July 1994
Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system
Journal of Mathematical Physics
March 1994
Linear r-matrix algebra for classical separable systems
Journal of Physics A General Physics
January 1994
Coexistence in the Competition Model with Diffusion
Journal of Differential Equations
January 1994
Quantum Lattices
January 1994
Elliptic solutions and blow-up in an integrable Hénon–Heiles system
Proceedings of the Royal Society of Edinburgh Section A Mathematics
January 1994
Classical Poisson Structure for a Hierarchy of One–Dimensional Particle Systems Separab...
Journal of Nonlinear Mathematical Physics
January 1994
The quantum discrete self-trapping equation in the Hartree approximation
Physica D Nonlinear Phenomena
November 1993
Preface
Physica D Nonlinear Phenomena
September 1993
Solitons on lattices
Physica D Nonlinear Phenomena
September 1993
Linear r-matrix algebra for systems separable in parabolic coordinates
Physics Letters A
September 1993
Soliton bands in anharmonic quantum lattices
Physics Letters A
January 1993
Future Directions of Nonlinear Dynamics in Physical and Biological Systems
January 1993
Corrigendum to ‘A monotonicity theorem and its application to stationary solutions of t...
IMA Journal of Applied Mathematics
January 1993
Quantum Solitons in the DNLS and Hubbard Models
January 1993
Membrane conductances involved in amplification of small signals by sodium channels in ...
The Journal of Physiology
October 1992
There's more than one way to skin Schrödinger's cat
Physica D Nonlinear Phenomena
October 1992
On ultrasonic Davydov solitons and the Hénon-Heiles system
Physics Letters A
June 1992
A monotonicity theorem and its application to stationary solutions of the phase field m...
IMA Journal of Applied Mathematics
January 1992
Structure of solution manifolds in a strongly coupled elliptic system
IMA Journal of Numerical Analysis
January 1992
Binding energies for discrete nonlinear Schrödinger equations
Physica Scripta
December 1991
Solitary waves on a strongly anisotropic KP lattice
Physics Letters A
August 1991
Proof of a conjecture by Scott concerning energy levels in the quantum DST equation
Physics Letters A
May 1991
Calculation of families of solitary waves on discrete lattices
Physics Letters A
September 1990
The quantum theory of local modes in a coupled system of nonlinear oscillators
Nonlinearity
May 1990
Introduction to the Discrete Self-Trapping Equation
January 1990
Understanding Steady-State Bifurcation Diagrams for a Model Reaction-Diffusion System
January 1990
Local modes in molecules
Journal of Molecular Liquids
October 1989
Stationary states associated with phase separation in a pure material. I. The large lat...
Physics Letters A
July 1989
On a stationary state characterization of transition from spinodal decomposition to nuc...
Physics Letters A
February 1989
Energy levels of the quantized discrete self-trapping equation
Journal of Biological Physics
January 1989
Biomolecular dynamics by computer analysis
Journal of Computational and Applied Mathematics
June 1988
Numerical Studies of Symmetry-Breaking Bifurcations in Reaction-Diffusion Systems
January 1988
Numerical Studies of Bifurcation in Reaction-Diffusion Models Using Pseudo-Spectral and...
January 1987
The quantized discrete self-trapping equation
Physics Letters A
December 1986
On the CH stretch overtones of benzene
Chemical Physics Letters
November 1986
A comparison of basis functions for the pseudo-spectral method for a model reaction-dif...
Journal of Computational and Applied Mathematics
July 1986
The Pseudo-Spectral Method and Path Following in Reaction-Diffusion Bifurcation Studies
SIAM Journal on Scientific and Statistical Computing
April 1986
The discrete self-trapping equation
Physica D Nonlinear Phenomena
July 1985
Pattern selection and low-dimensional chaos in the driven damped two-dimensional sine-G...
Journal of Physics C Solid State Physics
June 1985
Stability of stationary solutions of the discrete self-trapping equation
Physics Letters A
May 1985
How good are one‐dimensional Josephson junction models?
Journal of Applied Physics
February 1985
Comparison between one‐dimensional and two‐dimensional models for Josephson junctions o...
Journal of Applied Physics
February 1985
Between the local-mode and normal-mode limits
Chemical Physics Letters
January 1985
Dodd, R. K. / Eilbeck, J. C. / Gibbon, J. D. / Morris, H. C., Solitons and Nonlinear Wa...
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathem...
January 1985
Soliton structure in crystalline acetanilide
October 1984
A collocation approach to the numerical calculation of simple gradients in reaction-dif...
Journal of Mathematical Biology
February 1983
Collocation with Quadratic and Cubic Splines
IMA Journal of Numerical Analysis
January 1982
Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusi...
Bulletin of Mathematical Biology
January 1982
Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusi...
Bulletin of Mathematical Biology
January 1982
Chapter VII A Strategy for Investigating Solutions of Coupled Nonlinear Diffusion Equat...
January 1982
Multiple frequency generation by bunched solitons in Josephson tunnel junctions
December 1981
Chaos in the inhomogeneously driven sine-Gordon equation
Physics Letters A
December 1981
A mathematical model for pattern formation in biological systems
Physica D Nonlinear Phenomena
August 1981
Pulse evolution on coupled nerve fibres
Bulletin of Mathematical Biology
July 1981
Pulse evolution on coupled nerve fibres
Bulletin of Mathematical Biology
January 1981
A mathematical model for embryonic cell division based on a surface “cleavage field”
Journal of Theoretical Biology
November 1978
Numerical Studies of Solitons
January 1978
Numerical evidence for breakdown of soliton behaviour in solutions of the Maxwell-Bloch...
Physics Letters A
July 1977
Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
Journal of Computational Physics
January 1977
A modified regularized long-wave equation with an exact two-soliton solution
Journal of Physics A General Physics
October 1976
Numerical study of the regularized long-wave equation I: Numerical methods
Journal of Computational Physics
September 1975
The sine-Gordon equation as a model classical field theory
Il Nuovo Cimento B
February 1975
Exact Multisoliton Solution of the Reduced Maxwell-Bloch Equations of Non-linear Optics
IMA Journal of Applied Mathematics
January 1974
A general theory of self-induced transparency
Optical and Quantum Electronics
January 1974
N-Soliton solutions of some non-linear dispersive wave equations of physical significance
January 1974
AnN-soliton solution of a nonlinear optics equation derived by a general inverse method
Lettere al Nuovo Cimento
November 1973
Solitons in nonlinear optics. I. A more accurate description of the 2π pulse in self-in...
Journal of Physics A Mathematical Nuclear and General
September 1973
Multiple soliton and bisoliton bound state solutions of the sine-Gordon equation and re...
Journal of Physics A Mathematical Nuclear and General
August 1973
Exact multisoliton solution of the inhomogeneously broadened self-induced transparency ...
Journal of Physics A Mathematical Nuclear and General
May 1973
Exact Multisoliton Solutions of the Self-Induced Transparency and Sine-Gordon Equations
Physical Review Letters
February 1973
The asymptotic form of the N soliton solution of the Korteweg-de Vries equation
December 1972
A possible N soliton solution for a nonlinear optics equation
November 1972
Reflection of short pulses in linear optics
September 1972
The method of characteristics in the theory of resonant or nonresonant nonlinear optics
June 1972
Nonlinear radiation reaction, superradiance, and coherent optical pulse propagation
IEEE Journal of Quantum Electronics
June 1972
Calculation of the ϱ and Δ trajectories
Nuclear Physics B
February 1972
Table errata: {\it Higher transcendental functions. Vol. I, II}\ (McGraw-Hill, New York...
Mathematics of Computation
September 1971
Numerical studies of solitons on lattices
Quantum Breathers in an Attractive Fermionic Hubbard Model
2-D Breathers and Applications