Phase Shifts during Interaction between Two Solitons in Two-Dimensional Dusty Plasma

The dust acoustic solitary waves propagating in two different directions in two-dimensional dusty plasma are investigated. In order to study the
soliton interactions in multi-dimensional systems, we extend the reductive perturbation method and obtain two Korteweg--de Vries equations for nonlinear waves in both the ξ and η directions, respectively. The phase shifts after collision of two solitons with arbitrary angle are given. Finally, the solution of n_d up to O(ε⁴) order is obtained.