This concise review aims to provide a summary of the most relevant recent experimental and
theoretical results for solitons, ie self-trapped bound states of nonlinear waves, in two-and …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

We address the existence and stability of localized modes in the framework of the fractional
nonlinear Schrödinger equation (FNSE) with the focusing cubic or focusing-defocusing …

Optical lattices provide a key enabling and controllable platform for exploring new physical
phenomena and implications of degenerate quantum gases both in the quantum and …

In this paper, we investigate the new two-Lévy-index fractional nonlinear Schrödinger
(FNLS) equations with optical lattices, where two fractional derivative terms are introduced to …

Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose
strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various …

We study ordinary solitons and gap solitons (GS's) in the framework of the one-dimensional
Gross-Pitaevskii equation (GPE) with a combination of both linear and nonlinear lattice …

We demonstrate that the fractional cubic-quintic nonlinear Schrödinger equation,
characterized by its Lévy index, maintains ring-shaped soliton clusters (“necklaces") carrying …

By means of analytical and numerical methods, we address the modulational instability (MI)
in chiral condensates governed by the Gross-Pitaevskii equation including the current …

We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the
dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open …