Interaction Solution Of Nonlinear Systems

This paper mainly studies the(3+1)-dimensional nonlinear evolution equation and the AB-mKdV equation,and finds three kinds of interaction solutions respectively.We first use the binary Bell polynomial to transform the reduced(3+1)-dimensional nonlinear evolution equation into a bilinear form and find the lump solution.This type of lump solution is proposed by Chen Yong,Ma Wenxiu,etc.We have expanded it,obtained a lump solution with more parameters.Then,we use the lump solution to get the lumpoff solution,rogue solution,and the instanton solution.All of these can be interacted with by lump and line soliton,and have very interesting properties.We have made some analysis.Next,we analyze the AB-mKdV equation and the AKNS system.The AB-mKdV equation is proposed by Lou Senyue,which is of great significance for solving the physical problems of the two places.We first construct the nonlocal symmetry of the AKNS system and then localize it.Finally,the interaction solution of the AB-mKdV equation is obtained by Backlund transfor-mation of the AB-mKdV equation and the AKNS system:the interaction of the kink soliton and the bell-shaped soliton,the interaction of kink soliton and periodic waves,the interaction of bell-shaped soliton and periodic waves.