Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

This article offers a comprehensive survey of results obtained for solitons and complex
nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially …

Matter waves inside periodic potentials are well known from solid-state physics, where
electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates …

In this work, we present new two-mode extension to the coupled KdV–Schrodinger
equations. This new model arises in many applications in the field of optics, communications …

We study 1D trapped Bose gases in the strongly interacting regime. The systems are created
in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy …

Bose-Einstein condensates of rubidium atoms are stored in a two-dimensional periodic
dipole force potential, formed by a pair of standing wave laser fields. The resulting potential …

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional
equations are well known in anomalous diffusion. We connect these two fields by presenting …

Fractional order differential equations are utilized for modeling many complicated physical
and natural phenomena in nonlinear sciences and related fields. In this manuscript, the …

We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a
one-dimensional optical lattice. Making use of the small momentum spread of a BEC and …

Purpose: In this article, we establish novel solutions for the perturbed nonlinear Lenells
equation, which is one of the model to investigate soliton dynamics through a polarization …