Creating oscillons and oscillating kinks in two scalar field theories.

Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in 1+1 spatiotemporal dimensions. The solutions contain a control parameter, the variation of which produces oscillons and kinks with a flat-top shape. The model finds applications in condensed matter, cosmology, and high-energy physics.

Wide vector solitons in systems with time- and space-modulated nonlinearities.

In this work we apply point canonical transformations to solve some classes of two coupled nonautonomous nonlinear Schrödinger equations with specific cubic and quintic-time- and space-dependent-nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities.