106 citations · 508 across the 18 of their papers we have counts for
18 papers
Theory of Heat Equations for Sigma Functions
J. C. Eilbeck, J. Gibbons, Y. Ônishi +1
We consider the heat equations satisfied by the sigma function associated with a planar curve, extending and developing earlier pioneering work of Buchstaber and Leykin. These heat…
Nonlinear propagating localized modes in a 2D hexagonal crystal lattice
J. Bajars, J. C. Eilbeck, B. Leimkuhler
In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating…
Periods of second kind differentials of (n,s)-curves
J. C. Eilbeck, K. Eilers, V. Z. Enolski
For elliptic curves, expressions for the periods of elliptic integrals of the second kind in terms of theta-constants, have been known since the middle of the 19th century. In this…
Breathers and kinks in a simulated crystal experiment
Q. Dou, J. Cuevas, J. C. Eilbeck +1
We develop a simple 1D model for the scattering of an incoming particle hitting the surface of mica crystal, the transmission of energy through the crystal by a localized mode, and…
Abelian functions associated with genus three algebraic curves
J. C. Eilbeck, M. England, Y. Onishi
We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowe…
Sigma, tau and Abelian functions of algebraic curves
J. C. Eilbeck, V. Z. Enolski, J. Gibbons
We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve…