Interactions between solitons and the coherent oscillation structures generated by localized
disturbances via modulational instability are studied within the framework of the focusing …

We characterize the properties of the asymptotic stage of modulational instability arising
from localized perturbations of a constant background, including the number and location of …

We report results of the analysis for families of one-dimensional (1D) trapped solitons,
created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear …

Solitary waves in conservative and near-conservative systems may become unstable due to
a resonance of two internal oscillation modes. We study the parametrically driven, damped …

In this paper, we have investigated by numerical solution of the basic equation as well as by
the dynamical model the influence of higher-order effects on the dissipative soliton mapping …

We present a detailed analysis of the modulational instability (MI) of ground-state bright
solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the …

A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The
nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or …

The modulational instability (MI) phenomenon in the nonlinear Schrödinger equation
(NLSE) extended by two different nonlinear dispersion terms and the gradient term is …

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics
describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is …

We investigate the dynamics of optical soliton formation in media with quadratic nonlinearity
under conditions of long-living oscillations produced by the soliton's internal modes. We …