We investigate the fundamental phenomenon of the spontaneous, noise-induced
modulational instability (MI) of a plane wave. The statistical properties of the noise-induced …

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of
weakly interacting solitons in the framework of Korteweg–de Vries (KdV) equation. In this …

Reservoir computing is a promising framework that facilitates the approach to physical
neuromorphic hardware by enabling a given nonlinear physical system to act as a …

We study numerically the properties of (statistically) homogeneous soliton gas depending on
soliton density (proportional to number of solitons per unit length) and soliton velocities, in …

We study numerically the integrable turbulence in the framework of the one-dimensional
nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach …

Nondeterministic giant waves, denoted as rogue, killer, monster, or freak waves, have been
reported in many different branches of physics. Their physical interpretation is however still …

We propose an experiment for forming matter-wave soliton molecules. In the proposed
setup, we show that if two solitons are initially prepared in phase and with a sufficiently small …

A method for the description of the N-soliton interaction, which generalizes in a natural way
the Karpman-Solov'ev one for the nonlinear Schrödinger (NLS) equation, is proposed. Using …

Self-similar propagation of optical beams inside a one-dimensional nonlinear graded-index
waveguide amplifier is studied. By employing the lens-type and Husimi transformations …

Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are
studied. It is first shown that these interactions exhibit similar fractal dependence on initial …