The phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …

In the present work, we attempt a brief summary of various areas where non-linear waves
have been emerging in the phenomenology of lattice dynamical systems. These areas …

Motivated by recent experimental results, we study beating dark–dark (DD) solitons as a
prototypical coherent structure that emerges in two-component Bose–Einstein condensates …

This paper is devoted to studying the complete integrable Wadati–Konno–Ichikawa
equation, which is an important integrable model with physical background. Based on the …

We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a
class of Fermi–Pasta–Ulam lattices representing an uncompressed chain of beads …

We predict that one-and two-dimensional self-bound quantum droplets, forming in Bose–
Einstein condensates in the presence of Lee–Huang–Yang (LHY) quantum corrections to …

We consider standing lattice solitons for discrete nonlinear Schrödinger equation with
saturation (NLSS), where so-called transparent points were recently discovered. These …

We study the existence, stability, and mobility of fundamental discrete solitons in two-and
three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing …

In the present article, we study the standing wave problem for the discrete nonlinear
Schrödinger equation i ψn=−(∆ ψ) n+ vnψn− fn (ψn), n∈ Z,(1.1) where (∆ ψ) n= ψn+ 1+ ψn …

The main result of the paper concerns the existence of nontrivial exponentially decaying
solutions to periodic stationary discrete nonlinear Schrödinger equations with saturable …