Dual self-accelerating properties of one-dimensional finite energy Pearcey beam

Based on potential-free linear Schrödinger equation, we investigate the dynamics of one-dimensional finite energy Pearcey beam in free space. The result shows that the Pearcey beam evolves in the form of two-dimensional Pearcey function and exhibits a dual self-accelerating behavior. Moreover, the reason of dual self-accelerating behavior is also presented. The result shows that the one-dimensional finite energy Pearcey beam can be decomposed into two Airy-like beams accelerating in the opposite direction, and this acceleration leads to dual self-accelerating behavior of Pearcey beam.