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 Poincar\'{e}--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.