Rapidly growing demands for fast information processing have launched a race for creating
compact and highly efficient optical devices that can reliably transmit signals without losses …

Topological photonics has emerged recently as a novel approach for realizing robust optical
circuitry, and the study of nonlinear effects in topological photonics is expected to open the …

We review the design, theory, and applications of two dimensional periodic lattices hosting
conical intersections in their energy-momentum spectrum. The best known example is the …

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D)
space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC) …

We elaborate a mechanism for the formation of stable solitons of the semivortex type (with
vorticities 0 and 1 in their two components), populating a finite band gap in the spectrum of …

We derive nonlinear wave equations describing the propagation of slowly varying wave
packets formed by topological valley-Hall edge states. We show that edge pulses break up …

When using Laguerre and Hermite spectral methods to numerically solve PDEs in
unbounded domains, the number of collocation points assigned inside the region of interest …

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-
site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI) …

Nonlinearities in lattices with topological band structures can induce topological interfaces in
the bulk of structures and give rise to bulk solitons in the topological bandgaps. Here we …

We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic
nonlinearity. We show that with the nonlinearity parameters specifically tuned, a high degree …