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
A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely...A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.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,
基金Supported by National Natural Science Foundation of China under Grant Nos.11171312 and 11126308Science and Technology Research Key Projects of the Education Department of Henan Province under Grant No.12A110023
文摘A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.
