Helmholtz bright and boundary solitons

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently-reported Helmholtz bright solitons, for this type of polynomial non-linearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterpart

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media

"Light bullets" are multi-dimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced-transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multi-dimensional generalization of the one-dimensional Sine-Gordon soliton.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1]

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency

PACAP centrally mediates emotional stress-induced corticosterone responses in mice

Pituitary adenylate cyclase-activating polypeptide (PACAP) is a pleiotropic neuropeptide widely distributed in the nervous system. Recently, PACAP was shown to be involved in restraint stress-induced corticosterone release and concomitant expression of the genes involved in hypothalamic–pituitary–adrenal (HPA) axis activation. Therefore, in this study, we have addressed the types of stressors and the levels of the HPA axis in which PACAP signaling is involved using mice lacking PACAP (PACAP−/−). Among four different types of stressors, open-field exposure, cold exposure, ether inhalation, and restraint, the corticosterone response to open-field exposure and restraint, which are categorized as emotional stressors, but not the other two, was markedly attenuated in PACAP−/− mice. Peripheral administration of corticotropin releasing factor (CRF) or adrenocorticotropic hormone induced corticosterone increase similarly in PACAP and wild-type mice. In addition, the restraint stress-induced c-Fos expression was significantly decreased in the paraventricular nucleus (PVN) and medial amygdala (MeA), but not the medial prefrontal cortex, in PACAP−/− mice. In the PVN of PACAP−/− mice, the stress-induced c-Fos expression was blunted in the CRF neurons. These results suggest that PACAP is critically involved in activation of the MeA and PVN CRF neurons to centrally regulate the HPA axis response to emotional stressors

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. [S1050-2947(98)51110-9]

Introductory lectures on lattice QCD at nonzero baryon number

These lecture notes contain an elementary introduction to lattice QCD at nonzero chemical potential. Topics discussed include chemical potential in the continuum and on the lattice; the sign, overlap and Silver Blaze problems; the phase boundary at small chemical potential; imaginary chemical potential; and complex Langevin dynamics. An incomplete overview of other approaches is presented as well. These lectures are meant for postgraduate students and postdocs with an interest in extreme QCD. A basic knowledge of lattice QCD is assumed but not essential. Some exercises are included at the end