Individual Solitons Research Articles

Soliton interaction in optical fibers

Interactions of solitons generated by pairs of optical pulses are studied using the perturbed nonlinear Schrödinger equation, which models nonlinear optical pulses in a monomode fiber. We examine the mechanism of the soliton interaction both analytically and numerically and show that a bound 2-soliton splits into individual solitons traveling with different speeds because of higher-order effects. The numerical results are in extremely close agreement with those obtained recently by Mitschke and Mollenauer in their experiments on 2-solitons in optical fibers [Opt. Lett. 12, 355 (1987)].

Nonlinear pulse propagation in a monomode dielectric guide

We derive the nonlinear wave equation for an envelope of an electromagnetic wave in a monomode dielectric waveguide. Concrete examples are given for a single-mode optical fiber where the coefficients of resultant nonlinear Schrödinger equation with higher-order dispersion and dissipation (both linear and nonlinear) are given in terms of properties of the eigenfunction of the guided wave as well as of the material nonlinearity and dispersion. Using a newly-developed perturbation method, we show that the higher-order dispersions (linear and nonlinear) perserve the profile of a single soliton but to split up a bound <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> soliton ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \geq 2</tex> ) into individual solitons with different heights which propagate at different velocities. We also show that the higher-order nonlinear dissipation due to the induced Raman effect downshifts the carrier frequency of a single soliton in proportion to the distance of propagation and to the fourth power of the soliton amplitude.

Resonant interaction of ion-acoustic solitons in three-dimensions revisited

Using a launching structure consisting of four large diameter hemispherical grids located at the corners of a square, it is observed that the amplitude of a resonantly produced soliton is greater than ten times the value of an individual soliton. This observation extends to three dimensions Kaup’s conjecture that the two-dimensional resonance-soliton creation requires a finite interaction tune.

Solitons in superfluid 4He films

The Korteweg-de Vries (KdV) equation is derived from Landau two-fluid hydrodynamics applied to the thickness oscillation of the superfluid 4He film at low temperatures, where the main restoring force is van der Waals attraction from the substrate and the thermomechanical force due to phonons is a small correction. Since the usual third-sound generators and detectors are far wider than the individual solitons, the asymptotic solution of the KdV equation provided by the inverse scattering method is coarse-grained by regarding it as a continuous train of sharp pulses. The envelope so obtained still shows a singular front proportional to (t−t0)−1/2, where t0 is the arrival time of the fastest soliton, and should therefore be observable with the appropriate experimental arrangement.