Stability of optical gap solitons is analyzed within a coupled-mode theory. Lower intensity solitons are shown to always possess a vibration mode responsible for their long-lived oscillations. As the intensity of the soliton is increased, the vibration mode falls into resonance with two branches of the long-wavelength radiation producing a cascade of oscillatory instabilities of higher intensity solitons.[S0031-9007 (98)06265-6] PACS numbers: 42.65.Tg, 03.40.Kf, 05.45.+b, 75.30.Ds In the late 1970s and early 1980s, the theory of elementary particles [1] and condensed matter physics (in particular, the Su-Schrieffer-Heeger polyacetylene model [2]) stimulated a wide interest in particlelike solutions of classical spinor field equations. Recently there has been a remarkable upsurge of the interest; the localized solutions of spinorlike systems have made a comeback under the new name of gap solitons.Thanks to the gap in the linear spectrum, solitons in spinorlike systems can propagate without losing their energy to resonantly excited radiation waves [3,4]. An example of the gap-soliton bearing system is given by an optical fiber with periodically varying refractive index [3]; here the gap is produced by the Bragg reflection and resonance of the waves along the grating. Another class of gap solitons arises in two-wave resonant optical materials with a x ͑2͒ susceptibility and diatomic crystal lattices (see [4] and references therein). Finally, in the already mentioned polyacetylene model [2], the gap in the electron spectrum is due to the electron-phonon interaction and effective period doubling of the lattice.The aim of this Letter is to analyze the stability of gap solitons. Previous analytical studies of the spinor soliton stability faced serious obstacles (cf.[5]), while results of computer simulations were contradictory (cf. [6,7]). As a result, no stability or instability criterion is available to date. The main difficulty of the previous analyses was that they were all based on a postulate that stable solutions must render the energy minimum. In the actual fact, however, the minimality of energy is not necessary for stability in systems with indefinite metrics [8]. As far as optical gap solitons are concerned, they have been commonly deemed stable following recent computer simulations carried out for certain particular parameter values [9]. In this Letter we demonstrate that the gap solitons can be unstable, elucidate the mechanism of instability, and demarcate the stability/instability regions on the plane of their parameters.In nonlinear optics the gap solitons are usually analyzed within the coupled-mode theory [3] which reduces to a system of coupled equations for the amplitudes of the forward-and backward-propagating waves, i͑u t 1 u x ͒ 1 y 1 ͑jyj 2 1 rjuj 2 ͒u 0 , i͑y t 2 y x ͒ 1 u 1 ͑juj 2 1 rjyj 2 ͒y 0 .In the periodic Kerr medium one typically has r 1͞2 [3]; in other problems of the fiber optics r may range up to infinity [10]. In the case r 0 Eqs. (1) yield the massive Thirring model of the field the...

Results of charge form factors calculations for several unstable neutron-rich isotopes of light, medium, and heavy nuclei (He, Li, Ni, Kr, Sn) are presented and compared to those of stable isotopes in the same isotopic chain. For the lighter isotopes (He and Li) the proton and neutron densities are obtained within a microscopic large-scale shell-model, while for heavier ones Ni, Kr, and Sn the densities are calculated in deformed self-consistent mean-field Skyrme HF+BCS method. We also compare proton densities to matter densities together with their rms radii and diffuseness parameter values. Whenever possible comparison of form factors, densities and rms radii with available experimental data is also performed. Calculations of form factors are carried out both in plane wave Born approximation (PWBA) and in distorted wave Born approximation (DWBA). These form factors are suggested as predictions for the future experiments on the electron-radioactive beam colliders where the effect of the neutron halo or skin on the proton distributions in exotic nuclei is planned to be studied and thereby the various theoretical models of exotic nuclei will be tested.

Nucleus-Nucleus Scattering in the High-Energy Approximation and the Optical Folding PotentialFor the nucleus-nucleus scattering, the complex potential is obtained which corresponds to the eikonal phase of an optical limit of the Glauber-Sitenko high-energy approximation. The potential does not include free parameters, its real and imaginary parts depend on energy and are determined by the reported data on the nuclear density distributions and nucleon-nucleon scattering amplitude. Alternatively, for the real part, the folding potential can be utilized which includes the effective NN -forces and the exchange term, as well. As a result, the microscopic optical potential is constructed where contributions of the calculated real and imaginary parts are formed by fitting the two respective factors. An efficient of the approach is confirmed by agreements of calculations with the experimental data on elastic scattering cross-sections.The investigation has been performed at the Bogoliubov Laboratory of Theoretical Physics, JINR. ‚´ ¸ÉµÖÐ¥°· ¡µÉ¥ ³Ò ¶·¥¤² £ ¥³ ³¨±·µ¸±µ ¶¨Î¥¸±¨° ¶µ¤Ìµ¤, £¤¥ ± ± ¢¥Ð¥¸É¢¥´´ Ö, É ±¨³´¨³ Ö Î ¸ÉÓ ¶µÉ¥´Í¨ ² ¢ÒΨ¸²ÖÕɸִ ¡ §¥ ³¨±·µ-±µ ¶¨Î¥¸±¨Ì ³µ¤¥²¥°. ' Ôɵ°Í¥²ÓÕ¨¸ ¶µ²Ó §Ê¥É¸Ö µ ¶É¨Î¥¸±¨° ¶µÉ¥´Í¨ ², ±µ-ɵ·Ò°³µ¦´µ´ °É¨± ± ɵδµ¥¸µµÉ¢¥É¸É¢¨¥ µ ¶É¨Î¥¸±µ³Ê ¶·¥¤¥²Ê ³¨±·µ¸±µ- ¶¨Î¥¸±µ°³µ¤¥²¨· ¸¸¥Ö´¨Ö ¢ ¢Ò¸µ±µÔ´¥·£¥É¨Î¥¸±µ³ ¶·¨¡²¨¦¥´¨¨(‚), ¶·¥¤²µ¦¥´´µ°¢´ Î ²¥ ƒ² Ê¡¥·µ³¨'¨É¥´±µ ¤²Ö ¤·µ´-Ö¤¥·´µ£µ · ¸¸¥Ö´¨Ö [10, 11], ¶µ §¤´¥¥ µ¡µ¡Ð¥´´µ°´ ¸²ÊÎ °· ¸¸¥Ö´¨Ö Ö¤¥· [12,13]. ‚ ·Ö¤¥ ²ÊÎ ¥¢ ¤²Ö · ¸Î¥É ¢¥Ð¥¸É¢¥´´µ°Î ¸É¨ ¶µÉ¥´Í¨ ² ³Ò¨¸ ¶µ²Ó §Ê¥³ É ±¦¥ OE""¸ÊΥɵ³ µ¡³¥´ ´Ê±²µ´ ³¨. ÉµÉ ³ É¥·¨ ²¨ §²µ¦¥´¢ · §¤. 1¨2. ‚ · §¤. 3 ¶·¨¢µ¤ÖÉ¸Ö · ¸Î¥ÉÒ É ±¨Ì ¶µÉ¥´Í¨ ²µ¢, ¶·¥¤² £ ¥É¸Ö ³µ¤¥²Ó ¶µ¤£µ´±¨, ±µ£¤ ¢ ·Ó¨·ÊÕÉ¸Ö ¤¢ ´µ·³¨·ÊÕÐ¨Ì ³´µ¦¨É¥²Ö, µ ¶·¥¤¥²ÖÕÐ¨Ì ¢±² ¤ ¢¥Ð¥-É¢¥´´µ°¨³´¨³µ°Î ¸É¨ ¶µÉ¥´Í¨ ² , ¤ ´µ¸· ¢´¥´¨¥¸Ô±¸ ¶¥·¨³¥´É ²Ó´Ò³¥ Î¥´¨Ö³¨Ê ¶·Ê£µ£µ · ¸¸¥Ö´¨Ö.

Small-angle neutron scattering (SANS) on the unilamellar vesicle (ULV) populations (diameter 500 and 1,000 A) in D2O was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases: gel Lbeta', ripple Pbeta' and liquid Lalpha. Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the separated form factor (SFF) model. Vesicle shape changes from nearly spherical in the Lalpha phase to elliptical in the Pbeta' and Lbeta' phases. This is true for vesicles prepared via extrusion through pores with the diameter 500 A. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration and the surface area of the lipid molecule) were determined on the basis of the hydrophobic-hydrophilic (HH) approximation of neutron scattering length density across the bilayer rhox and of the step function (SF) approximation of rhox. DMPC membrane thickness in the Lalpha phase (T = 30 degrees C) demonstrates a dependence on the membrane curvature for extruded vesicles. Prepared via extrusion through 500 A diameter pores, vesicle population in the Lalpha phase has the following characteristics: average value of minor semi-axis 266 +/- 2 A, ellipse eccentricity 1.11 +/- 0.02, polydispersity 26%, thickness of the membrane 48.9 +/- 0.2 A and of the hydrophobic core 19.9 +/- 0.4 A, surface area 60.7 +/- 0.5 A2 and number of water molecules 12.8 +/- 0.3 per DMPC molecule. Vesicles prepared via extrusion through pores with the diameter 1,000 A have polydispersity of 48% and membrane thickness of 45.5 +/- 0.6 A in the Lalpha phase. SF approximation was used to describe the DMPC membrane structure in Lbeta' (T = 10 degrees C) and Pbeta' (T = 20 degrees C) phases. Extruded DMPC vesicles in D2O have membrane thickness of 49.6 +/- 0.5 A in the Lbeta' phase and 48.3 +/- 0.6 A in the Pbeta' phase. The dependence of the DMPC membrane thickness on temperature was restored from the SANS experiment.

No abstract

Since solitons of the parametrically driven damped nonlinear Schrödinger equation do not have oscillatory tails, it was suggested that they cannot form bound states. We show that this equation does support solitonic complexes, with the mechanism of their formation being different from the standard tail-overlap mechanism. One of the arising stationary complexes is found to be stable in a wide range of parameters, others unstable. PACS numbers: 42.65.Tg, 05.45.Yv Motivation.-Bound states of solitons and solitary pulses are attracting increasing attention in nonlinear optics [1-5], dynamics of fluids [6-9], and excitable media [10]. Stable bound states can compete with free solitons as alternative attractors. This is detrimental in nonlinear optics, for example, where the interaction between adjacent pulses poses limitations to the stable operation of transmission lines and information storage elements. Unstable solitonic complexes are not meaningless either; they serve as intermediate states visited by the system when in the spatiotemporal chaotic regime.Here, we consider solitonic complexes in the parametrically driven damped nonlinear Schrödinger equation,

Abstract. Calculations of microscopic optical potentials (OP's) (their real and imaginary parts) are performed to analyze the 6 He+p elastic scattering data at a few tens of MeV/nucleon (MeV/N). The OP's and the cross sections are calculated using three model densities of 6 He. Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OP's, as well as effects of their renormalization are studied. The sensitivity of the cross sections to the nuclear densities was tested and one of them that gives a better agreement with the data was chosen.

Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton's response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton's temporal chaos to the homoclinic bifurcation.