一个可积耦合离散方程的多孤子解和守恒律

Multiple soliton solutions and conservation laws of an integrable coupled discrete equation

基于一个可积耦合离散方程的Lax对与一次Darboux变换,构造该离散方程的N-波Darboux变换和无穷守恒律。通过应用Darboux变换,得到方程的多孤子解,最后通过图像研究了孤子解的性质,讨论了多孤子之间的非弹性碰撞作用现象,这些解和所得到的作用现象对于理解一些物理现象有所帮助。

Based on Lax representation and a single Darboux transformation,the N-fold Darboux transformation and infinite conservation laws of the discrete equation are constructed. By applying Darboux transformation,the discrete multi-soliton equation in terms of Vandermonde-type determinant is derived. Some inelastic interaction evolution phenomena arising for the two,three and four-soliton solutions are studied graphically. All these solutions and properties may contribute to the explanation of some physical phenomena.