Research paperBright and dark soliton solutions to the AB system and its multi-component generalization

•Bright soliton and dark soliton solutions in the Gram determinant form are constructed from Hirota method and Sato theory.•Soliton dynamics of one-soliton and two-soliton are investigated.•Multi-component generalization is given and shown to be integrable with Lax pairs.•N−soliton solutions to the coupled AB system is presented in Pfaffian expression.

The determinant structures to the AB system are derived by using Hirota method and reduction technique from Sato theory. N-bright soliton solutions to the focusing and N−dark soliton solutions to the defocusing AB system are provided respectively. A multi-component AB system is proposed and shown to be integrable with Lax pairs. Solutions to the multi-component system are presented in terms of Pfaffians.