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

In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

In quantum interferometry, it is vital to control and utilize nonlinear interactions for the
achievement of high-precision measurements. Due to their long coherence time and high …

All stationary solutions to the one-dimensional nonlinear Schrödinger equation under box
and periodic boundary conditions are presented in analytic form. We consider the case of …

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types
in the general (nonintegrable) model of a spinor (three-component) model of the Bose …

We develop a systematic analytical approach to consider the dynamics of linear and
nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with …

We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under
gravity in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. Our …

Binary Bell polynomials are extended to systematically construct bilinear formalism, bilinear
Bäcklund transformations, Lax pairs with multi-parameters and infinite conservation laws of …

We discuss a method to create two-dimensional (2D) traps as well as atomic shell, or
bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic …

The variable-coefficient Korteweg–de Vries (KdV)-typed models, although often hard to be
studied, are of current interest in describing various real situations. Under investigation …