The interaction of nonlinear waves in two-dimensional dust crystals

This paper investigates the collision between two nonlinear waves with different propagation directions in two-dimensional dust crystals. Using the extended Poincaré--Lighthill-Kuo perturbation method, two Korteweg--de Vries equations for nonlinear waves in both the ξ and eta directions are obtained, respectively, and the analytical phase shifts and trajectories after the collision of two nonlinear waves are derived. Finally, the effects of parameters of the lattice constant a, the arbitrary constant u_0η, the forces f(r), and the colliding angle θ on the phase shifts of both colliding nonlinear waves are examined.