Biomedical subjects
Publications and source records attributed to Y B Gaididei.
Collapse of (2+1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrödinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may be arrested under certain circumstances.
The discrete nonlinear Schrödinger equation with competing short-range and long-range interactions is considered in spatial dimensions d> or =2. This model equation is derived for a situation of two linearly coupled excitations (independently of dimension), and we analytically and numerically study its properties in 2+1 dimensions. We analyze theoretically and demonstrate numerically the dependence of the discrete breather solutions on the amplitude and range of the interactions. We find that complete suppression of the existence thresholds obtained recently for short-range interactions can be achieved beyond a critical value of the amplitude or of the range of the long-range kernel. For supercritical values of the corresponding parameters, staggered branches of solutions are obtained both in theory as well as in the numerical experiment.
Collapse of (1+1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrödinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up may be delayed and even arrested.
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system.