Adaptive femtosecond pulse shaping to control supercontinuum generation in a microstructure fiber

Efficient confinement of laser radiation in the core of a photonic crystal fiber increases the nonlinear processes resulting in supercontinuum generation. The technique of adaptive pulse shaping using an evolutionary algorithm provides a method to gain control over such highly nonlinear processes. Adaptive pulse shaping of the driving laser radiation passing through the photonic crystal fiber is employed to modify the shape and composition of the output supercontinuum. Amplitude and phase shaping are used to optimize the broadband emission between 500 and 700 nm, as well as a soliton centered at 935 nm. The intensities of the emission and of the soliton driven by a shaped laser pulse increase in comparison to an unshaped pulse by factors of 4 and 3, respectively. The spectral width in the range of 500-600 nm is increased by approximately 40%. In addition, the suppression of self-steepening effects in supercontinuum spectra is demonstrated.     

10 Gbps optical soliton transmission link using in-line SOA on standard SMF at 1.3 μm

In this paper, 10 Gbps optical soliton transmission link using in-line semiconductor optical amplifiers (SOAs) for already installed standard single mode fibers (SMF) at 1.3 μm wavelength has been reported. The pattern effect and the impact of chirp on pulse propagation after amplification have been investigated. The observations are based on modeling and simulation optical soliton transmission link. Optical soliton pulse transmission over distances of the order of several hundreds of kilometers has been shown with and without initial chirp.     

Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su–Gardner (or one-dimensional Green–Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular bore” stage of the evolution. The resulting formula represents a “non-integrable” analogue of the well-known semi-classical distribution for the Korteweg–de Vries equation, which is usually obtained through the inverse scattering transform. Our analytical results are shown to agree with the results of direct numerical simulations of the Su–Gardner system. Our analysis can be generalised to other weakly dispersive, fully nonlinear systems which are not necessarily completely integrable.     

LETTER: Soliton Solution in Dilaton—Maxwell Gravity

The inverse scattering problem method application to the construction of exact solutions, for the Maxwell dilaton gravity system is considered. By use of Belinsky and Zakharov L-A pair the solution of the theory is constructed. The rotating Kerr-like configuration with NUT-parameter is obtained.     

A note on a paper by A.G. Bratsos, M. Ehrhardt and I.Th. Famelis

In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. 197(1) (2008) 190-205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived.     

Properties of nano-scale soliton-like excitations in two-dimensional lattice layers

Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.     

Interaction properties of complex modified Korteweg-de Vries (mKdV) solitons

Interaction properties of complex solitons are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries (mKdV) equation, given by the Hirota equation and the Sasa-Satsuma equation, which share the same traveling wave (single-soliton) solution having a sech profile characterized by a constant speed and a constant phase angle. For both equations, nonlinear interactions in which a fast soliton collides with a slow soliton are shown to be described by 2-soliton solutions that can have three different types of interaction profile, depending on the speed ratio and the relative phase angle of the individual solitons. In all cases, the shapes and speeds of the solitons are found to be preserved apart from a shift in position such that their center of momentum moves at a constant speed. Moreover, for the Hirota equation, the phase angles of the fast and slow solitons are found to remain unchanged, while, for the Sasa-Satsuma equation, the phase angles are shown to undergo a shift such that the relative phase between the fast and slow solitons changes sign.     

Combined Wronskian solutions to the 2D Toda molecule equation

By combining two pieces of bi-directional Wronskian solutions, molecule solutions in Wronskian form are presented for the finite, semi-infinite and infinite bilinear 2D Toda molecule equations. In the cases of finite and semi-infinite lattices, separated-variable boundary conditions are imposed. The Jacobi identities for determinants are the key tool employed in the solution formulations.     

Bright-soliton collisions with shape change by intensity redistribution for the coupled Sasa–Satsuma system in the optical fiber communications

By means of symbolic computation and Darboux transformation, analytically and numerically investigated in this paper is a two-coupled Sasa–Satsuma system, which can describe the pulse propagation in birefringent fibers, so as to increase the bit rate in optical fibers, or achieve wavelength-division multiplexing. Analytical bright N-soliton solution of the system is firstly derived. Based on the bright one- and two-soliton solutions, numerical simulation and figure illustration are carried out on through the multi-parametric management, i.e., different choices among eight parameters in the two-soliton solutions. The interaction mechanisms for the bright two-solitons are revealed in three aspects: Separating evolution behaviors, elastic collision behaviors and inelastic collision behaviors. There exist three different cases for the inelastic collision for the two-soliton, which reflect correspondingly different energy transfer mechanisms (by intensity redistribution) between the two components: Manakov-typed collision; a near-elastic collision and another completely inelastic collision between the two components; and four single-solitons in two components undergo shape changes (inelastic and elastic) due to intensity redistribution, where one single-soliton keeps invariant and the other three single-solitons change during the collision. The collision mechanisms may be viewed as the two-solitons interact in a waveguide supporting propagation of two nonlinear waves simultaneously. In general, partial suppression (enhancement) of intensity between the components is dependent on the values of the soliton parameters.