形变Boussinesq型方程族及其守恒律和Darboux变换

A Deformed Boussinesq-Type Hierarchy, Conservation Laws and Darboux Transformation

该文借助于零曲率方程得到了一个与3×3矩阵谱问题相关的形变Boussinesq型非线性演化可积方程族.通过考虑两个线性谱问题,给出了方程族中前两个方程的无穷多守恒律.借助于Darboux变换得到了第一个形变Boussinesq型方程的一些显式解.

In this paper,we propose a deformed Boussinesq-type integrable hierarchy of nonlinear evolution equations associated with a 3×3 matrix spectral problem by using the zero-curvature equation.Based on two linear spectral problems,we obtain the infinite many conservation laws of the first two members in the hierarchy.Some explicit solutions to the first deformed Boussinesq-type equation are given by utilizing the Darboux transformation.