We present an overview of nonlinear phenomena related to optical quadratic solitons—
intrinsically multi-component localized states of light, which can exist in media without …

We predict that photonic moiré patterns created by two mutually twisted periodic sublattices
in quadratic nonlinear media allow the formation of parametric solitons under conditions that …

Interest in physical systems with fractional derivatives has exploded in the 21st century.
Similarly, interest in the localized excitations of nonlinear dynamical systems continues to …

We report on the existence and stability of multicolor lattice vortex solitons constituted by
coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic …

We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type
(DNLS) equations. For a conservative system, we consider the global in time solvability and …

We study the existence and stability of localized states in the discrete nonlinear Schrödinger
equation on two-dimensional nonsquare lattices. The model includes both the nearest …

Topological insulators are unique physical structures that are insulators in their bulk, but
support currents at their edges which can be unidirectional and topologically protected from …

We study the mobility of solitons in lattices with quadratic (χ (2), alias second-harmonic-
generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic …

We introduce the notion of a PT-symmetric dimer with a χ (2) nonlinearity. Similarly to the
Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical …

Gap Solitons in Periodic Discrete Schrödinger Equations with Nonlinearity Page 1 Acta Appl
Math (2010) 109: 1065–1075 DOI 10.1007/s10440-008-9360-x Gap Solitons in Periodic Discrete …