D-brane on deformed AdS3 × S3

We study D1-brane in AdS3 × S3κ-deformed background with non-trivial dilaton and Ramond-Ramond fields. We consider purely time-dependent and spatially-dependent ansatz where we study the solutions of the equations of motion for D1-brane in given background. We find that the behavior of these solutions crucially depends on the value of the parameter a that was introduced in [7].