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

Zero curvature representation for a new fifth-order integrable system

In this brief note we present a zero-curvature representation for one of the new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure

Plane wave limit of local conserved charges

We study the plane wave limit of the Backlund transformations for the classical string in AdS space times a sphere and obtain an explicit expression for the local conserved charges. We show that the Pohlmeyer charges become in the plane wave limit the local integrals of motion of the free massive field. This fixes the coefficients in the expansion of the anomalous dimension as the sum of the Pohlmeyer charges.Comment: v2: added explanation

Noise-Induced Transition from Translational to Rotational Motion of Swarms

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.Comment: 7 pages, 7 figure

Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality

Detailed quantitative predictions are obtained for phonon and multiphonon excitations in well-deformed rotor nuclei within the geometric framework, by exact numerical diagonalization of the Bohr Hamiltonian in an SO(5) basis. Dynamical gamma deformation is found to significantly influence the predictions through its coupling to the rotational motion. Basic signatures for the onset of rigid triaxial deformation are also obtained.Comment: 17 pages, 10 figures; to be published Phys. Rev.

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations