Nonlinear classical Hamiltonian lattices exhibit generic solutions—discrete breathers. They
are time-periodic and (typically exponentially) localized in space. The lattices have discrete …

We present a progress overview focused on the recent theoretical and experimental
advances in the area of soliton manipulation in optical lattices. Optical lattices offer the …

We show theoretically that a photonic topological insulator can support edge solitons that
are strongly self-localized and propagate unidirectionally along the lattice edge. The …

It is shown that the concept of topological phase transitions can be used to design nonlinear
photonic structures exhibiting power thresholds and discontinuities in their transmittance …

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 …

In this work, we present a mechanical example of an experimental realization of a stability
reversal between on-site and intersite centered localized modes. A corresponding …

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 elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an
appropriately modified definition of the Riesz fractional derivative, which is characterized by …

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 study experimentally and theoretically discrete solitons in crystalline structures
consisting of several tens of laser-cooled ions confined in a radio frequency trap. Resonantly …