Multi-solitary waves for the nonlinear Klein-Gordon equation

International audienceWe consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Analytic theory of narrow lattice solitons

The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice minimum. This instability can, however, be so weak that the soliton is ``mathematically unstable'' but ``physically stable''. Stability of solitons centered at a lattice minimum depends on the dimension of the problem and on the nonlinearity. In the subcritical and supercritical cases, the lattice does not affect the stability, leaving the solitons stable and unstable, respectively. In contrast, in the critical case (e.g., a cubic nonlinearity in two transverse dimensions), the lattice stabilizes the (previously unstable) solitons. The stability in this case can be so weak, however, that the soliton is ``mathematically stable'' but ``physically unstable''

The Air Microwave Yield (AMY) experiment - A laboratory measurement of the microwave emission from extensive air showers

The AMY experiment aims to measure the microwave bremsstrahlung radiation (MBR) emitted by air-showers secondary electrons accelerating in collisions with neutral molecules of the atmosphere. The measurements are performed using a beam of 510 MeV electrons at the Beam Test Facility (BTF) of Frascati INFN National Laboratories. The goal of the AMY experiment is to measure in laboratory conditions the yield and the spectrum of the GHz emission in the frequency range between 1 and 20 GHz. The final purpose is to characterise the process to be used in a next generation detectors of ultra-high energy cosmic rays. A description of the experimental setup and the first results are presented.Comment: 3 pages -- EPS-HEP'13 European Physical Society Conference on High Energy Physics (July, 18-24, 2013) at Stockholm, Swede

The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Orbital stability: analysis meets geometry

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the wave equation, and for the Manakov system

Sensory profiles and preference analysis in ornamental horticulture: The case of the rosebush

The context of ornamental horticulture is considered in order to extend the techniques of sensory and preference evaluation by taking the rosebush as a plant model. In a preliminary study (Boumaza, Demotes-Mainard, Huché-Thélier, & Guérin, 2009), a sensory evaluation was conducted in order to set up a list of attributes. Subsequently, this list was adapted to assess 10 rosebushes. After the control of the panel performance using a multivariate strategy of analysis, the average scores were used in product mapping. The evaluation of the preferences with regard to these rosebushes was undertaken: 253 subjects were asked to rank the products by decreasing order of liking. Thereafter, the preference data were subjected to an internal preference mapping and a cluster analysis. Six homogeneous segments of consumers were eventually retained. By way of performing an external preference mapping, the average ranks were regressed upon the sensory attributes using principal component regression: the preferences of 67% of the consumers were satisfactorily explained by the attributes

A search for point sources of EeV photons

Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10^17.3 eV to 10^18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm^-2 s^-1, and no celestial direction exceeds 0.25 eV cm^-2 s^-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.Comment: 28 pages, 10 figures, accepted for publication in The Astrophysical Journa