Multiscale expansions avector solitons of a two‐dimensional nonlocal nonlinear Schrödinger system. Issue 4 (5th August 2020)

• Record Type: Journal Article
• Authors: Koutsokostas, Georgios N.; Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.; Prinari, Barbara; Biondini, Gino
• Is Part Of: Studies in applied mathematics. Volume 145:Issue 4(2020)
• Page Start: 739
• Page End: 764
• Publication Date: 2020-08-05
• Subjects: dark and antidark solitons -- KP equations -- multiple scales analysis -- nonlocal coupled NLS; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12334
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: 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.