Collisional dynamics of solitons in the coupled PT symmetric nonlocal nonlinear Schrödinger equations

•We investigate a model which describes the PT symmetric coupled nonlocal NLS equation.•We show the model completely integrable by constructing the associated Lax-pair.•We show the described PT symmetric model admits both bright and dark solitons for the same nonlinearity.•We also show how one can convert the bright bound state into dark bound state and vice versa. We investigate the focussing coupled PT symmetric nonlocal nonlinear Schrödinger equation employing Darboux transformation approach. We find a family of exact solutions including pairs of Bright-Bright, Dark-Dark and Bright-Dark solitons in addition to solitary waves. We show that one can convert bright bound state onto a dark bound state in a two soliton solution by selectively finetuning the amplitude dependent parameter. We also show that the energy in each mode remains conserved unlike the celebrated Manakov model. We also characterize the behaviour of the soliton solutions in detail. We emphasize that the above phenomenon occurs due to the nonlocality of the model.