Observation of off-axis solitary waves propagating along a specific trajectory in photorefractive crystals.

We report the propagation dynamics of swallowtail beams (SBs) within a photorefractive crystal. In the nonlinear regime, the self-accelerating and secondary self-focusing features of the swallowtail beams are influenced, and a solitary wave is generated. The main lobe energy of the swallowtail beams is guided to a specific inclined trajectory, leading to a stable solitary wave, and we control the output position of the solitary wave by changing the launch angle.