Soliton scattering in noncommutative spaces

We discuss exact multisoliton solutions of integrable hierarchies on noncommutative space–times in various dimensions. The solutions are represented by quasideterminants in compact forms. We study soliton scattering processes in the asymptotic region where the configurations can be real-valued. We find that the asymptotic configurations in the soliton scatterings can all be the same as commutative ones, i.e., the configuration of an $N$-soliton solution has $N$ isolated localized lumps of energy, and each solitary wave-packet lump preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. As new results, we present multisoliton solutions of the noncommutative anti-self-dual Yang–Mills hierarchy and discuss two-soliton scattering in detail.