The coupled semi-discrete modified Korteweg-de Vries equation in (2+1)-dimensions is proposed, it is shown that it, can be decomposed into two (1+1)-dimensional differential-difference equations belonging to mKd...The coupled semi-discrete modified Korteweg-de Vries equation in (2+1)-dimensions is proposed, it is shown that it, can be decomposed into two (1+1)-dimensional differential-difference equations belonging to mKdV lattice hierarchy by considering a discrete isospeetral problem. A Darboux transformation is set up for the resulting (2+1)- dimensional lattice soliton equation with the help of gauge transformations of Lax pairs. As an illustration by example, the soliton solutions of the mKdV lartice equation in (2+1)-dimensions are explicitly given,展开更多
基金The roject partially supported by National Natural Science Foundation of China under Grant No. 60572113
文摘The coupled semi-discrete modified Korteweg-de Vries equation in (2+1)-dimensions is proposed, it is shown that it, can be decomposed into two (1+1)-dimensional differential-difference equations belonging to mKdV lattice hierarchy by considering a discrete isospeetral problem. A Darboux transformation is set up for the resulting (2+1)- dimensional lattice soliton equation with the help of gauge transformations of Lax pairs. As an illustration by example, the soliton solutions of the mKdV lartice equation in (2+1)-dimensions are explicitly given,