Parallel Solitons Research Articles

Interactions of bright solitons for the (2+1)-dimensional coupled nonlinear Schrödinger equations from optical fibres with symbolic computation

In nonlinear optical fibres, the evolution of two polarization envelopes is governed by a system of coupled nonlinear Schrödinger (CNLS) equations. In this paper, with the aid of symbolic computation, the analytical bright one- and two-soliton solutions of the (2+1)-dimensional CNLS equations under certain constraints are presented by employing the Hirota method. We have discussed the head-on and overtaking interactions which include elastic and inelastic collisions between two parallel bright solitons. In the interaction process, the intensities of solitons can exhibit various redistributions. We also point out that these properties have important physical applications in constructing various logic gates and nonlinear optical fibers.

Optical Logic Arrays with Weak Beams Guided by Bright-Spatial Solitons

A basic four-bit logic optical array prototype operating with weak beams guided by brightspatial solitons is proposed. The operation principle of the device is based on the crossing of spatial solitons, which guide the weak beam, over two parallel and well separated solitons. Selecting appropriate phase difference values of parallel solitons, the energy of the weak beam can be transferred into them to produce the four binary logic states: (0,0), (1,0), (0,1) and (1,1).

Dromion-like structures in a (3+1)-dimensional KdV-type equation

Dromion structures have been found in many (2 + 1)-dimensional models. The similar structure in (3 + 1) dimensions is studied in this paper for a KdV-type equation, . Starting from the bilinear form of the model, we found that there are five types of multi-dromion solutions for its potentials, say, . The first type of multi-dromion solution is driven by multi-camber solitons with one of them being non-parallel to the x-axis. The second, third and fourth types of multi-dromion solutions are driven by two camber solitons and one, two and three sets of parallel plane solitons, respectively. The fifth type of multi-dromion solution is driven by one set of parallel plane solitons, one set of camber solitons which are parallel to the x-axis and one camber soliton which is non-parallel to the x-axis. Phase shifts may be involved in the interactions among the multi-dromions for the first and fifth types of solutions. A single dromion solution of the model may possess quite a free shape. For instance, the point-like dromions, ring-type dromions, extended and sharp dromions and oscillatory dromions can be obtained by selecting some arbitrary functions appropriately.

Coupling between parallel dark spatial soliton waveguides

Dark spatial solitons are able to guide light in a self-defocusing Kerr-type medium by inducement of a refractive-index profile equivalent to a dielectric waveguide. We derive the coupling coefficients between two parallel dark soliton waveguides and investigate the coupling length as a function of various dark soliton and guided-wave parameters.

The quantum inverse method and the monodromy matrix in integrable field theories

Under investigation in this paper is a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model describing certain situations from the fluid mechanics, ocean dynamics and plasma physics. N-fold Darboux transformation (DT) of a variable-coefficient Ablowitz–Kaup–Newell–Segur spectral problem is constructed via a gauge transformation. Multi-solitonic solutions in terms of the double Wronskian for the vc-mKdV model are derived by the reduction of the N-fold DT. Three types of the solitonic interactions are discussed through figures: (1) Overtaking collision; (2) Head-on collision; (3) Parallel solitons. Nonlinear, dispersive and dissipative terms have the effects on the velocities of the solitonic waves while the amplitudes of the waves depend on the perturbation term.

The Bäcklund trasnformation for the integrable many-body systems

Under investigation in this paper is a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model describing certain situations from the fluid mechanics, ocean dynamics and plasma physics. N-fold Darboux transformation (DT) of a variable-coefficient Ablowitz–Kaup–Newell–Segur spectral problem is constructed via a gauge transformation. Multi-solitonic solutions in terms of the double Wronskian for the vc-mKdV model are derived by the reduction of the N-fold DT. Three types of the solitonic interactions are discussed through figures: (1) Overtaking collision; (2) Head-on collision; (3) Parallel solitons. Nonlinear, dispersive and dissipative terms have the effects on the velocities of the solitonic waves while the amplitudes of the waves depend on the perturbation term.