The interaction of nonlinear waves in two-dimensional lattice

This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincaré--Lighthill--Kuo perturbation method, it obtains two Korteweg--de Vries equations for nonlinear waves in both the \xi and \eta directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u(v) up to O(\epsilon^3) order is given.