Title: General $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations,
Abstract: 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.