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Multiscale expansions avector solitons of a two‐dimensional nonlocal nonlinear Schrödinger system
Author(s) -
Koutsokostas Georgios N.,
Horikis Theodoros P.,
Frantzeskakis Dimitrios J.,
Prinari Barbara,
Biondini Gino
Publication year - 2020
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12334
Subject(s) - quantum nonlocality , soliton , cartesian coordinate system , integrable system , physics , nonlinear system , nonlinear schrödinger equation , schrödinger's cat , classical mechanics , mathematical analysis , mathematical physics , quantum mechanics , mathematics , geometry , quantum , quantum entanglement
One‐ and two‐dimensional solitons of a multicomponent nonlocal nonlinear Schrödinger (NLS) system are constructed. The model finds applications in nonlinear optics, where it may describe the interaction of optical beams of different frequencies. We asymptotically reduce the model, via multiscale analysis, to completely integrable ones in both Cartesian and cylindrical geometries; we thus derive a Kadomtsev‐Petviashvili equation and its cylindrical counterpart, Johnson's equation. This way, we derive approximate soliton solutions of the nonlocal NLS system, which have the form of: (a) dark or antidark soliton stripes and (b) dark lumps in the Cartesian geometry, as well as (c) ring dark or antidark solitons in the cylindrical geometry. The type of the soliton, namely dark or antidark, is determined by the degree of nonlocality: dark (antidark) soliton states are formed for weaker (stronger) nonlocality. We perform numerical simulations and show that the derived soliton solutions do exist and propagate undistorted in the original nonlocal NLS system.