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Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations
Author(s) -
Prinari Barbara,
Ortiz Alyssa K,
Mee Cornelis,
Grabowski Marek
Publication year - 2018
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.12223
Subject(s) - inverse scattering transform , spinor , integrable system , soliton , inverse scattering problem , nonlinear system , mathematical physics , scattering , physics , matrix (chemical analysis) , quantum inverse scattering method , inverse , bose–einstein condensate , mathematics , mathematical analysis , quantum mechanics , geometry , composite material , materials science
Abstract The inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger‐type systems whose reductions include two equations that model certain hyperfine spin F = 1 spinor Bose–Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four‐component fermionic condensates. In addition, the general behavior of the soliton solutions for all four reductions is analyzed in detail, and some novel solutions are presented.