Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions
- 10.1080/14029251.2020.1683996How to use a DOI?
- Inverse scattering transform; nonlinear waves; solitons; nonlinear Schrödinger systems
The inverse scattering transform (IST) with nonzero boundary conditions at infinity is developed for a class of 2 × 2 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 our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows us to develop the IST on the standard complex plane instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity, symmetries and asymptotics of the scattering eigenfunctions and scattering data are derived, and properties of the discrete spectrum are analyzed in detail. In addition, the general behavior of the soliton solutions for all four reductions is discussed, and some novel soliton solutions are presented.
- © 2020 The Authors. Published by Atlantis and Taylor & Francis
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TY - JOUR AU - Alyssa K. Ortiz AU - Barbara Prinari PY - 2019 DA - 2019/10/25 TI - Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions JO - Journal of Nonlinear Mathematical Physics SP - 130 EP - 161 VL - 27 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2020.1683996 DO - 10.1080/14029251.2020.1683996 ID - Ortiz2019 ER -