The Interaction Of Nonlinear Waves In Two-dimensional Lattice

Soliton is a universal and important nonlinear phenomenon.In decades,soliton in lattice systems became an active research realm.We should note that studies of the interaction between solitons are frequently reported in recent years.In this paper,By using the extended Poincare-Lighthill-Kuo perturbation method,we theoretically study the interaction between two solitons in two-dimensional(2D) lattice,some significant results are presented.The thesis consists of four chapters:In chapter one,we briefly introduce the basic theoretical concept of soliton,the history,present status and significance of the study of solitons.Chapter two is devolved to depicting the solitons in lattice.In Chapter three,the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice is investigated.By using the extended Poincare-Lighthill-Kuo method, two Korteweg-de Vries equations for nonlinear waves in both theξandηdirections are obtained,respectively,and the analytical phase shifts after the collision of two nonlinear waves are derived.Finally,the solution of u(v) up to O(∈³) order is given.In chapter four, the collision between two nonlinear waves with different propagation directions in two-dimensional dust crystal is investigated.By using the extended Poincare-Lighthill-Kuo perturbation method,we obtain two Korteweg-de Vries equations for nonlinear waves in both theξandηdirections,respectively.We also obtain the approximated analytical results of the phase shifts and trajectories of both solitary waves after the collision of two solitary waves.Finally,the effects of parameters of the lattice constant a,the arbitrary constant u_0η,the forces f(r),and the colliding angleθon the phase shifts of both colliding nonlinear waves are examined.Finally,we summarize the present thesis and give an outlook of the future study in this field.