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

Beam Intensity and Energy Control for the SPIRAL2 Facility

TUPB029 - ISBN 878-3-95450-122-9International audienceThe first part of the SPIRAL2 facility, which entered last year in the construction phase at GANIL in France, consists of an ion source, a deuteron and a proton source, a RFQ and a superconducting linear accelerator delivering high intensities, up to 5 mA and 40 MeV for the deuteron beams. Diagnostic developments have been done to control both beam intensity and energy by non-interceptive methods at the linac exit. The beam current is measured by using couples of ACCT-DCCT installed along the lines and the beam energy by using a time of flight device. This paper gives explanations about the technical solutions, the results and resolutions for measuring and controlling the beam

Measurement and Control of the Beam Energy for the SPIRAL2 Accelerator

WEPF32, http://accelconf.web.cern.ch/AccelConf/ibic2013/International audienceThe first part of the SPIRAL2 facility, which entered last year in the construction phase at GANIL in France, will be composed of an ion source, a deuteron/proton source, a RFQ and a superconducting linear accelerator delivering high intensities, up to 5 mA and 40MeV for the deuteron beams. As part of theMEBT commissioning, the beam energy will be measured on the BTI (Bench of Intermediate Test) at the exit of the RFQ. At the exit of the LINAC, the system has to measure but also control the beam energy. The control consists in ensuring that the beam energy is under a limit by taking account of the measurement uncertainty. The energy is measured by a method of time of flight, the signal is captured by non-intercepting capacitive pick-ups. This paper presents also the results obtained in terms of uncertainties and dynamics of measures

Instability and stability properties of traveling waves for the double dispersion equation

In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms $u_{xxxx}$ and $u_{xxtt}$. We obtain an explicit condition in terms of $a$, $b$ and $p$ on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up. In the special case of the Boussinesq equation ($b=0$), our condition reduces to the one given in the literature. For the double dispersion equation, we also investigate orbital stability of traveling waves by considering the convexity of a scalar function. We provide both analytical and numerical results on the variation of the stability region of wave velocities with $a$, $b$ and $p$ and then state explicitly the conditions under which the traveling waves are orbitally stable.Comment: 16 pages, 4 figure

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

Configuration mixing in 188^{188}Pb : band structure and electromagnetic properties

In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model.Comment: submitted to pr

Progress on the Beam Energy Monitor for the SPIRAL2 Accelerator.

WEPF29, posterInternational audienceThe first part of the SPIRAL2 project entered last year in the end of the construction phase at GANIL in France. The facility will be composed by an ion source, a deuteron/proton source, a RFQ and a superconducting linear accelerator. The driver is planned to accelerate high intensities, up to 5 mA and 40 MeV for the deuteron beams. A monitoring system was built to measure the beam energy on the BTI line (Bench of Intermediate Test) at the exit of the RFQ. As part of theMEBT commissioning, the beamenergy will be measured on the BTI with an Epics monitoring application. At the exit of the LINAC, another system will have to measure and control the beam energy. The control consists in ensuring that the beam energy stays under a limit by taking account of the measurement uncertainty. The energy is measured by a method of time of flight; the signal is captured by non-intercepting capacitive pick-ups. This paper describes the BTI monitor interface and presents the system evolution following the design review

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''

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure