We study a fractional reaction–diffusion system with two types of variables: activator and
inhibitor. The interactions between components are modeled by cubical nonlinearity …

We study the topological physics in nonlinear Schrödinger systems on lattices. We employ
the quench dynamics to explore the phase diagram, where a pulse is given to a lattice point …

Discrete systems with long-range interactions are considered. Continuous medium models
as continuous limit of discrete chain system are defined. Long-range interactions of chain …

We study the nonlinear effect on topological edge states by including a nonlinear term to a
Chern insulator which has two chiral edge states with opposite chiralities. We explore …

In this work, we introduce a spatially discrete model that is a modification of the well-known α-
Fermi–Pasta–Ulam chain with damping. The system is perturbed at one end by a harmonic …

Using the fact that extremum of variation of generalized action can lead to the fractional
dynamics in the case of systems with long-range interaction and long-term memory function …

We study the dynamics of the Schrödinger equation with a fractional Laplacian (− Δ) α, and
the decoherence of the solution is observed. Analytically, we obtain equations of motion for …

There are different approaches to discretization of the Schrödinger equation with some
approximations. In this paper we derive a discrete equation that can be considered as exact …

We study—experimentally, theoretically, and numerically—nonlinear excitations in lattices of
magnets with long-range interactions. We examine breather solutions, which are spatially …

We consider a chain of nonlinear oscillators with long-range interaction of the type 1∕ l 1+
α⁠, where l is a distance between oscillators and 0< α< 2⁠. In the continuous limit, the …