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.

Unstaggered-staggered solitons in two-component discrete nonlinear Schr\"{o}dinger lattices

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled by the repulsive cross-phase-modulation (XPM) interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite accurately, and are stable. Close to a boundary of the existence region of the solitons (which may feature several connected branches), there are broad solitons which are not well approximated by the VA, and are unstable

A model of a dual-core matter-wave soliton laser

We propose a system which can generate a periodic array of solitary-wave pulses from a finite reservoir of coherent Bose-Einstein condensate (BEC). The system is built as a set of two parallel quasi-one-dimensional traps (the reservoir proper and a pulse-generating cavity), which are linearly coupled by the tunneling of atoms. The scattering length is tuned to be negative and small in the absolute value in the cavity, and still smaller but positive in the reservoir. Additionally, a parabolic potential profile is created around the center of the cavity. Both edges of the reservoir and one edge of the cavity are impenetrable. Solitons are released through the other cavity's edge, which is semi-transparent. Two different regimes of the intrinsic operation of the laser are identified: circulations of a narrow wave-function pulse in the cavity, and oscillations of a broad standing pulse. The latter regime is stable, readily providing for the generation of an array containing up to 10,000 permanent-shape pulses. The circulation regime provides for no more than 40 cycles, and then it transforms into the oscillation mode. The dependence of the dynamical regime on parameters of the system is investigated in detail.Comment: Journal of Physics B, in pres

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

Helical vs. fundamental solitons in optical fibers

We consider solitons in a nonlinear optical fiber with a single polarization in a region of parameters where it carries exactly two distinct modes, the fundamental one and the first-order helical mode. From the viewpoint of applications to dense-WDM communication systems, this opens way to double the number of channels carried by the fiber. Aside from that, experimental observation of helical (spinning) solitons and collisions between them and with fundamental solitons are issues of fundamental interest. We introduce a system of coupled nonlinear Schroedinger equations for fundamental and helical modes, which have nonstandard values of the cross-phase-modulation coupling constants, and investigate, analytically and numerically, results of "complete" and "incomplete" collisions between solitons carried by the two modes. We conclude that the collision-induced crosstalk is partly attenuated in comparison with the usual WDM system, which sometimes may be crucially important, preventing merger of the colliding solitons into a breather. The interaction between the two modes is found to be additionally strongly suppressed in comparison with that in the WDM system in the case when a dispersion-shifted or dispersion-compensated fiber is used.Comment: a plain latex file with the text and two ps files with figures. Physica Scripta, in pres

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

On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources

Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called "squared solutions" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV equation. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV hierarchy with generic self-consistent sources are analyzed. This allows one to formulate a set of conditions on the perturbation terms that preserve the integrability. The perturbation corrections to the scattering data and to the corresponding action-angle variables are studied. The analysis shows that although many nontrivial solutions of KdV equations with generic self-consistent sources can be obtained by the Inverse Scattering Transform (IST), there are solutions that, in principle, can not be obtained via IST. Examples are considered showing the complete integrability of KdV6 with perturbations that preserve the eigenvalues time-independent. In another type of examples the soliton solutions of the perturbed equations are presented where the perturbed eigenvalue depends explicitly on time. Such equations, however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe

A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data

Quantum shock waves in the Heisenberg XY model

We show the existence of quantum states of the Heisenberg XY chain which closely follow the motion of the corresponding semi-classical ones, and whose evolution resemble the propagation of a shock wave in a fluid. These states are exact solutions of the Schroedinger equation of the XY model and their classical counterpart are simply domain walls or soliton-like solutions.Comment: 15 pages,6 figure