We present an experimental observation of an oscillating Kerr cavity soliton, ie, a time-
periodic oscillating one-dimensional temporally localized structure excited in a driven …

We show that parity-time-(PT-) symmetric coupled optical waveguides with gain and loss
support localized oscillatory structures similar to the breathers of the classical ϕ 4 model …

Chains of parametrically driven, damped pendula are known to support solitonlike clusters
of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently …

In this work, we have studied numerically the dynamics of the parametrically driven damped
nonlinear Schrödinger equation (PDDNLS). The PDDNLS is a universal model to describe …

In this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–
Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic …

Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation
are obtained as solutions of the boundary-value problem on a two-dimensional …

We employ global quasi-steady manifolds to rigorously reduce forced, linearly damped
dispersive partial differential equations to finite dimensional flows. The manifolds we …

We investigate the long-time evolution of weakly perturbed single-site breathers (localized
stationary states) in the discrete nonlinear Schrödinger equation. The perturbations we …

We present a uniform asymptotic expansion of the wobbling kink to any order in the
amplitude of the wobbling mode. The long-range behavior of the radiation is described by …

We show that the (undamped) parametrically driven nonlinear Schrödinger equation has
wide classes of traveling soliton solutions, some of which are stable. For small driving …