孤子方程广义的双Wronskian解(英文)

Wronskian技术是求解非线性偏微分方程精确解的直接而有效的方法之一.Wronskian解可以通过直接代入孤子方程的双线性方程中得到验证.将Wronskian元素满足的条件方程推广到任意矩阵方程,利用Wronskian技术,构造孤子方程的广义双Wronskian解.利用广义双Wronskian解可以得到孤子方程许多类型的精确解,如孤子解、有理解、周期解、Matveev解、complexiton解以及混合解.具体地研究了等谱Levi方程,得到了一些新的Wronskian恒等式,从而得到了Levi方程广义双Wronskian形式的精确解,并利用Wronskian技术对解进行了证明.

Generalized double Wronskian solutions of the soliton equations

Wronskian technique is one of efficient direct approaches to deriving exact solutions to nonlinear evolution equations.It provides direct verifications of solutions to bilinear equations of soliton equations.In this paper,we extend the equations satisfied by Wronskian entries to the arbitrary matrix equations and work out the general double Wronskian solutions of the soliton equations through the Wronskian technique.Furthermore,we can obtain more types exact solutions such as soliton solutions,rational solutions,periodic solutions,Matveev solutions,complexiton solutions and interaction solutions from the general double Wronskian solutions.Applications are made for the isospectral Levi equations and some determinantal identities are introduced.We present the exact solutions in general double Wronskian forms of the Levi equations and the solutions are verified by means of the Wronskian technique.