A fifth order semidiscrete mKdV equation  

作　　者：ZHOU Tong ZHU ZuoNong HE Peng 

机构地区：[1]Department of Mathematics,Shanghai Jiao Tong University

出　　处：《Science China Mathematics》2013年第1期123-134,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10971136);the Ministry of Education and Innovation of Spain (Grant No.MTM2009-12670)

摘　　要：In this paper, aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations, we construct a fifth order semidiscrete mKdV equation from the three known semidiscrete mKdV fluxes. We not only give its Lax pairs, Darboux transformation, explicit solutions and infinitely many conservation laws, but also show that their continuous limits yield the corresponding results for the fifth order mKdV equation. We thus conclude that the fifth order discrete mKdV equation is extremely an useful discrete scheme for the fifth order mtCdV equation.In this paper,aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations,we construct a fifth order semidiscrete mKdV equation from the three known semidiscrete mKdV fluxes.We not only give its Lax pairs,Darboux transformation,explicit solutions and infinitely many conservation laws,but also show that their continuous limits yield the corresponding results for the fifth order mKdV equation.We thus conclude that the fifth order discrete mKdV equation is extremely an useful discrete scheme for the fifth order mKdV equation.

关 键 词：fifth order semidiscrete mKdV equation Darboux transformation soliton solutions conversationlaws continuous limits 

分 类 号：O241.8[理学—计算数学]