Multiple Solitary Waves Research Articles

Multiple Solitary Waves For a Non-homogeneous Schrödinger–Maxwell System in ℝ3

Abstract We look for standing waves of nonlinear Schrödinger equation coupled with Maxwell’s equations. We use the variational formulation introduced by Benci and Fortunato in 1992 for studying an eigenvalue problem for the Schrödinger-Maxwell system in bounded domains. We establish the existence of multiple standing waves both in the homogeneous and the non-homogeneous cases by means of the fibering method introduced by Pohozaev.

Optical multisoliton generation in nematic liquid crystals.

The nonlocal nonlinearity stemming from molecular reorientation in nematic liquid crystals supports the formation of multiple solitary waves, following the onset of spatial modulational instability from both wide and focused input beams. We report experimental observations of such phenomena at power levels of hundreds of milliwatts in planar cells with a voltage bias.

Multiple Solitary Waves Due to Second-Harmonic Generation in Quadratic Media

A detailed mathematical analysis is undertaken of solitary-wave solutions of a system of coupled nonlinear Schrodinger equations describing second-harmonic generation in optical materials with χ(2) nonlinearity. The so-called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter α that includes both wave and material properties. Using methods from the calculus of variations, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive α . Recently, bound states (multipulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be α∈ (0,1), and the bifurcations occurring at the two extremes of this interval are uncovered.

Phase- and polarization-insensitive all-optical switching by self-guiding in quadratic media

We demonstrate numerically that a frequency-degenerate process through typeII downconversion in a quadratic nonlinear waveguide leads to the formation of spatial simultons and all-optical switching in the presence of a control signal. This novel effect is phase independent, generally insensitive to polarization, and weakly affected by the magnitude of the control input. Multiple solitary waves can also be obtained, depending on the details of the interaction.

Bidirectional soliton street

The bidirectional long-wave model introduced by Wu (1994)[1] and Yih & Wu (1995)[2] is applied to evaluate interactions between multiple solitary waves progressing in both directions in a uniform channel of rectangular cross-section and undergoing collisions of two classes, one being head-on and the other overtaking collisions between these solitons. For a binary head-on collision, the two interacting solitary waves are shown to merge during a phase-locking period from which they reemerge separated, each asymptotically recovering its own initial identity while both being retarded in phase from their original pathlines. For a binary overtaking collision between a soliton of height α1 overtaking a weaker one of height α1, the two solition peaks are shown to either pass through each other or remain separated throughout the encounter according as α1/α2 or <3, respectively. With no phase locking during the overtaking, the two solitary waves re-emerge afterwards with their initial forms recovered and with the stronger wave being advanced whereas the weaker one retarded in phase from their original pathlines. By extension, the theory is generalized to apply to uniform channels of arbitrary cross-sectional shape.