The present review summarizes experimental and theoretical work dealing with self-
organized solitary localized structures (LSs) that are observed in spatially extended …

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a
harmonic potential, which models a trapped atomic Bose-Einstein condensate, are …

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 …

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 …

Systems of solitary waves in the one-dimensional Gross-Pitaevskii equation, which models a
trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyze the …

We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in
multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave …

Under investigation in this paper is a discrete integrable Ablowitz–Ladik equation, which has
certain applications in the electrical and optical systems. Via the Hirota method and symbolic …

We develop a perturbation theory for bright solitons of the F= 1 integrable spinor Bose-
Einstein condensates (BEC) model. The formalism is based on using the Riemann-Hilbert …

Scattering of a matter-wave single soliton and two-soliton molecule incident on the modified
Pöschl-Teller potential well has been studied by means of a collective coordinate approach …