82 citations · 312 across the 8 of their papers we have counts for
8 papers
Solutions of the Differential Inequality with a~Null Lagrangian: Regularity and Removability of Singularities
A. A. Egorov
We prove a theorem on self-improving regularity for derivatives of solutions of the inequality constructed by means of a quasiconvex function and a null…
Surface vortex solitons
Yaroslav V. Kartashov, Alexey A. Egorov, Victor A. Vysloukh +1
We discover the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. Such solitons can feature strongly noncan…
Shaping soliton properties in optical Mathieu lattices
Yaroslav V. Kartashov, Alexey A. Egorov, Victor A. Vysloukh +1
We address basic properties and stability of two-dimensional solitons in photonic lattices induced by the nondiffracting Mathieu beams. Such lattices allow for smooth topological t…
Soliton topology versus discrete symmetry in optical lattices
Yaroslav V. Kartashov, Albert Ferrando, Alexey A. Egorov +1
We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the poss…
Stable multicolor periodic-wave arrays
Yaroslav V. Kartashov, Alexey A. Egorov, Anna S. Zelenina +2
We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a thresh…
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Yaroslav V. Kartashov, Alexey A. Egorov, Victor A. Vysloukh +1
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We…