The interaction of nonlinear waves in two-dimensional lattice

This paper investigates the collision between two nonlinear waveswith arbitrary angle in two-dimensional nonlinear lattice. By usingthe extended Poincar'{e}--Lighthill--Kuo perturbation method, itobtains two Korteweg--de Vries equations for nonlinear waves in boththe $xi$ and $eta$ directions, respectively, and derives theanalytical phase shifts after the collision of two nonlinear waves.Finally, the solution of $u(v)$ up to $O(epsilon^{3})$ order isgiven.