Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Shape coexistence in neutron-deficient Kr isotopes: Constraints on the single-particle spectrum of self-consistent mean-field models from collective excitations

We discuss shape coexistence in the neutron-deficient Kr72-Kr78 isotopes in the framework of configuration mixing calculations of particle-number and angular-momentum projected axial mean-field states obtained from self-consistent calculations with the Skyrme interaction SLy6 and a density-dependent pairing interaction. While our calculation reproduces qualitatively and quantitatively many of the global features of these nuclei, such as coexistence of prolate and oblate shapes, their strong mixing at low angular momentum, and the deformation of collective bands, the ordering of our calculated low-lying levels is at variance with experiment. We analyse the role of the single-particle spectrum of the underlying mean-field for the spectrum of collective excitations.Comment: accepted for publication in Phys. Rev.

On complete integrability of the Mikhailov-Novikov-Wang system

We obtain compatible Hamiltonian and symplectic structure for a new two-component fifth-order integrable system recently found by Mikhailov, Novikov and Wang (arXiv:0712.1972), and show that this system possesses a hereditary recursion operator and infinitely many commuting symmetries and conservation laws, as well as infinitely many compatible Hamiltonian and symplectic structures, and is therefore completely integrable. The system in question admits a reduction to the Kaup--Kupershmidt equation.Comment: 5 pages, no figure

Dynamics of broadband dispersive Alfven waves

The properties of amplitude modulated broadband Alfven waves is investigated. In particular, the dynamics of circularly polarized dispersive Alfven waves, governed by a derivative nonlinear Schroedinger equation, is analyzed using the Wigner formalism. The modulational instability of random phase dispersive pump Alfven waves is investigated, and it is shown that the spectral broadening gives rise to a new mode structure.Comment: 9 pages, 2 figures, to appear in Phys. Lett.

Renormalization Group Theory for a Perturbed KdV Equation

We show that renormalization group(RG) theory can be used to give an analytic description of the evolution of a perturbed KdV equation. The equations describing the deformation of its shape as the effect of perturbation are RG equations. The RG approach may be simpler than inverse scattering theory(IST) and another approaches, because it dose not rely on any knowledge of IST and it is very concise and easy to understand. To the best of our knowledge, this is the first time that RG has been used in this way for the perturbed soliton dynamics.Comment: 4 pages, no figure, revte

Base manifolds for fibrations of projective irreducible symplectic manifolds

Given a projective irreducible symplectic manifold $M$ of dimension $2n$, a projective manifold $X$ and a surjective holomorphic map $f:M \to X$ with connected fibers of positive dimension, we prove that $X$ is biholomorphic to the projective space of dimension $n$. The proof is obtained by exploiting two geometric structures at general points of $X$: the affine structure arising from the action variables of the Lagrangian fibration $f$ and the structure defined by the variety of minimal rational tangents on the Fano manifold $X$

Optical Bistability in Nonlinear Optical Coupler with Negative Index Channel

We discuss a novel kind of nonlinear coupler with one channel filled with a negative index material (NIM). The opposite directionality of the phase velocity and the energy flow in the NIM channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation

Quantized representation of some nonlinear integrable evolution equations on the soliton sector

The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple quantized representation of these equations and their soliton solutions over a Fock space of bosons or of fermions. The classical nonlinear wave equation becomes a nonlinear equation for an operator. The solution of this equation is constructed through the operator analog of the Hirota transformation. The classical N-solitons solution is the expectation value of the solution operator in an N-particle state in the Fock space.Comment: 12 page

Sinking and floating rates of natural phytoplankton assemblages in Lake Erken

Sinking rates of the <120 mu m size phytoplankton fraction of water from Lake Erken were determined during the summer 1992 by following the increase of chlorophyll a in the 10 ml-bottom layer in replicate 100 ml settling cylinders. Changes in chlorophyll a concentrations as a function of incubation time allowed two fractions to be separated. Fast sinking rates varied between values of 1.9 m/day when pennate and centric diatoms and coccal cyanobacteria were dominant tin cell concentration) and values of 0.5 m/day when cryptophytes and chrysophytes dominated the <120 mu m size fraction. Slow sinking rates decreased from 0.04 m/day at the beginning of July to 0.02 m/day in late July. Photosynthesis-Irradiance parameters (P-max(B) light saturated photosynthesis and #alpha#(B), light limited photosynthesis) were lower in the fast sinking fraction (P-max(B) = 1.3 - 2.4 mu gC/mu gChl/h and #alpha#(B) = 0.01 - 0.04 mu gC/mu gChl/h/(mu E/m(2)/s) than in the slow or non-sinking one (P-max(B) = 3.9 - 6.4 mu gC/mu gChl/h and #alpha#(B) = 0.03 - 0.08 mu gC/mu gChl/h/(mu E/m(2)/s). P-max(B) and #alpha#B of the planktonic Gloeotrichia echinulata, a colonial broom-forming cyanobacterium, were similar to those found in the fast sinking fraction. Mean floating rates of G. echinulata were around 43 m/d from 15 to 27 July and increased by a factor of two afterwards. G. echinulata colonies migrating upwards from sediments and captured in inverted traps showed a mean floating rate of 104 m/d