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- J C EILBECK
- 1999

- J. CHRIS EILBECK
- 2003

We review work on the Discrete Nonlinear Schrödinger (DNLS) equation over the last two decades.

Numerical predictions of a simple myelinated nerve fiber model are compared with theoretical results in the continuum and discrete limits, clarifying the nature of the conduction process on an isolated nerve axon. Since myelinated nerve fibers are often arranged in bundles, this model is used to study ephaptic (nonsynaptic) interactions between impulses on… (More)

- J C Eilbeck
- 1994

We give an analytical description of the locus of the two-gap ellip-tic potentials associated with the corresponding flow of the Calogero– Moser system. We start with the description of Treibich–Verdier two– gap elliptic potentials. The explicit formulae for the covers, wave functions and Lamé polynomials are derived, together with a new Lax representation… (More)

- J. C. Eilbeck, V. Z. Enolski, S. Matsutani, Y. Ônishi, E. Previato
- 2007

We develop the theory of generalized Weierstrass σ-and ℘-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential equations satisfied by the ℘-functions, a proof that the coefficients of the power series expansion of the σ-function are polynomials of coefficients of the defining… (More)

- J. C. EILBECK
- 2008

We develop the theory of Abelian functions defined using a tetrag-onal curve of genus six, with the specific example of the cyclic curve, y 4 = x 5 + λ 4 x 4 + λ 3 x 3 + λ 2 x 2 + λ 1 x + λ 0 discussed in detail. We define gener-alisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the… (More)

- J C Eilbeck, V Z Enol 'skii, V B Kuznetsov, A V Tsiganov
- 2008

We consider a hierarchy of the natural type Hamiltonian systems of n degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of 2 × 2 matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the… (More)

- J C Eilbeck, V Z Enolskii
- 2000

We use the bilinear operator formalism to derive a new representation of the power series for the Weierstrass σ function. It is not generally known that Baker solved a number of nonlinear integrable partial differential equations in 1907 [2]. In the course of an investigation of ultra-elliptic functions, he wrote certain relations between them, in which… (More)

- S Baldwin, J C Eilbeck, J Gibbons, Y ˆ Onishi
- 2006

We discuss the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the " purely trigonal " (or " cyclic trigonal ") curve y 3 = x 5 + λ 4 x 4 + λ 3 x 3 + λ 2 x 2 + λ 1 x + λ 0 is discussed in detail, including a list of some of the associated… (More)

- A. V. Savin, J. C. Eilbeck
- 1999

We study moving topological solitons (kinks and antikinks) in the nonlinear Klein-Gordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spectral method, the (anti)kink solutions with oscillating background (so-called nanopterons) are found as travelling waves of permanent… (More)