The solution to the Davey–Stewartson I equation is analyzed to show that the resonance between periodic soliton and growing-and-decaying mode exists. Under the quasi-resonant condition, the mode develops first in the one side region of the periodic soliton. The periodic soliton is accelerated as a result of the growth and decay of the mode existed in the region and the wave field shifts to the ...

A dark soliton becomes unstable when it is incident on a background density gradient, and the induced instability results in the emission of sound. Detailed quantitative studies of sound emission are performed for various potentials, such as steps, linear ramps and gaussian traps. Continuous emission of sound is found to lead to an apparent deformation of the soliton profile. The power emitted ...

Non-adiabatic pulse compression of cascaded higher-order optical soliton is investigated. We demonstrate high degree compression of pulses with soliton orders N=2, 3, 4, and 5 in two or three nonlinear fibers with different second-order dispersion coefficients. Each fiber length is shorter than half of its soliton period. This compression technique has significant advantages over the widely rep...

Feynman rules are derived for computing quantum corrections to the mass of a soliton in quantum field theory. These rules exhibit a finite propagator, but in contrast to previous methods, no additional effective vertices are introduced beyond those present in the original shifted Lagrangian. The derivation is based on imposing end-point boundary conditions appropriate to a soliton state on the ...

Optical soliton pulses offer great promise as a means for transmitting high data rate information in optical fibers over trans-oceanic distances. This thesis addresses two aspects of optical soliton communication. First, soliton propagation in the presence of a small-signal background continuum is discussed. It is essential to examine soliton-continuum interaction as it may lead to timing jitte...

We study dark soliton solutions of a multi-component Gross–Pitaevskii equation for hyperfine spin F = 1 spinor Bose–Einstein condensate. The interactions are supposed to be inter-atomic repulsive and anti-ferromagnetic ones of equal magnitude. The solutions are obtained from those of an integrable 2× 2 matrix nonlinear Schrödinger equation with nonvanishing boundary conditions. We investigate t...

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from...

This paper investigates a cylindrical nonlinear Schrödinger (cNLS) equation, which describes the cylindrically diverging quasi-plane envelope waves in a nonlinear medium. With the Hirota method and symbolic computation, bilinear form and N-soliton solutions in the form of an Nth-order polynomial in N exponentials are obtained for the cNLS equation. By means of the properties of double Wronskian...

Stable picosecond soliton transmission is demonstrated numerically by use of concatenated gain-distributed nonlinear amplifying fiber loop mirrors (NALMs). We show that, as compared with previous soliton transmission schemes that use conventional NALMs or nonlinear optical loop mirror and amplifier combinations, the present scheme permits a significant increase of loop-mirror (amplifier) spacin...

We discuss a novel type of surface soliton-aberrated surface soliton-appearance in a nonlinear one dimensional photonic crystal and a possibility of this surface soliton formation in two dimensional photonic crystal. An aberrated surface soliton possesses a nonlinear distribution of the wavefront. We show that, in one dimensional photonic crystal, the surface soliton is formed at the photonic c...