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...

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are ch...

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...

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrödinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the cor...

We consider N-soliton solutions of the KP equation, (−4ut + uxxx + 6uux)x + 3uyy = 0 . An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. The N-soliton solutions include all possible resonant interactions among those line solitons. We then classify those N-soliton solutions by defining a pair of N-numbers (n,n)...

We investigate the dynamics of solitons in generalized Klein-Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will ...