2017/12/04 by Yang, Jianke · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.1712.01181
General N-solitons in three recently-proposed nonlocal nonlinear Schrödinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schrödinger equations, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. It is shown that general N-solitons in these different equations can be derived from the same Riemann-Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann-Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of N-solitons in these equations is also explored. In all the three nonlocal equations, a generic feature of their solutions is repeated collapsing. In addition, multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.