J C Eilbeck

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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 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)
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)
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)
1. Voltage signals of about 1 mV evoked in photoreceptors of the drone honey bee by shallow modulation of a background illumination of an intensity useful for behaviour are thought to be amplified by voltage-dependent Na+ channels. To elucidate the roles of the various membrane conductances in this amplification we have studied the effects of the Na+(More)
  • P L Christiansen, J C Eilbeck, V Z Enolskii, N A Kostov
  • 2000
We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibres with strong birefringence, and two-mode optical fibres. Recently these equations appear as a model describing pulse-pulse interactions in(More)
  • J C Eilbeck, V Z Enol 'skii, V B Kuznetsov, D V Leykin
  • 1993
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2 × 2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is(More)