Self-trapping of light and nonlinear localized modes in 2D photonic crystals and waveguides

We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.Comment: 20 pages (LaTeX) with 12 figures (EPS

Models for energy and charge transport and storage in biomolecules

Two models for energy and charge transport and storage in biomolecules are considered. A model based on the discrete nonlinear Schrodinger equation with long-range dispersive interactions (LRI's) between base pairs of DNA is offered for the description of nonlinear dynamics of the DNA molecule. We show that LRI's are responsible for the existence of an interval of bistability where two stable stationary states, a narrow, pinned state and a broad, mobile state, coexist at each value of the total energy. The possibility of controlled switching between pinned and mobile states is demonstrated. The mechanism could be important for controlling energy storage and transport in DNA molecules. Another model is offered for the description of nonlinear excitations in proteins and other anharmonic biomolecules. We show that in the highly anharmonic systems a bound state of Davydov and Boussinesq solitons can exist.Comment: 12 pages (latex), 12 figures (ps

Solitons in anharmonic chains with ultra-long-range interatomic interactions

We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.Comment: 4 pages (LaTeX), 5 figures (Postscript); submitted to Phys. Rev.

Multi-soliton energy transport in anharmonic lattices

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.Comment: 4 pages, 4 figure

Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending decreases when curvature increases, i.e. bending manifests itself as a trap for excitations. Moreover, the potential of this trap is double-well, thus leading to a symmetry breaking phenomenon: a symmetric stationary state may become unstable and transform into an energetically favorable asymmetric stationary state. The essentials of symmetry breaking are examined analytically for a simplified model. We also demonstrate a threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving nonlinear excitation passing through the bending.Comment: 13 pages (LaTeX) with 10 figures (EPS

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.

Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks

We consider Klein-Gordon models with a $\delta$-correlated spatial disorder. We show that the properties of immobile kinks exhibit strong dependence on the assumptions as to their statistical distribution over the minima of the effective random potential. Namely, there exists a crossover from monotonically increasing (when a kink occupies the deepest potential well) to the non-monotonic (at equiprobable distribution of kinks over the potential minima) dependence of the average kink width as a function of the disorder intensity. We show also that the same crossover may take place with changing size of the system.Comment: 7 pages, 4 figure

Self-trapping and stable localized modes in nonlinear photonic crystals

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.Comment: 4 pages (RevTex) with 5 figures (EPS