TY - JOUR
T1 - Discrete and Semi-Discrete Multidimensional Solitons and Vortices
T2 - Established Results and Novel Findings
AU - Malomed, Boris A.
N1 - Publisher Copyright:
© 2024 by the author.
PY - 2024/2
Y1 - 2024/2
N2 - This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic ((Formula presented.)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its (Formula presented.) -symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and (Formula presented.) -symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
AB - This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic ((Formula presented.)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its (Formula presented.) -symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and (Formula presented.) -symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
KW - Bose–Einstein condensates
KW - PT symmetry
KW - Salerno model
KW - lattice dynamics
KW - nonlinear Schrödinger equations
KW - nonlinear optics
KW - quantum droplets
KW - skyrmions
KW - spin–orbit coupling
KW - vortices
UR - http://www.scopus.com/inward/record.url?scp=85185956367&partnerID=8YFLogxK
U2 - 10.3390/e26020137
DO - 10.3390/e26020137
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C2 - 38392392
AN - SCOPUS:85185956367
SN - 1099-4300
VL - 26
JO - Entropy
JF - Entropy
IS - 2
M1 - 137
ER -