Darboux Transformation And Infinitely Many Conservation Laws Of The Coupled Modified Korteweg-de Vries Equations Associated With3×3Matrix Spectral Problem

In this paper, a Darboux transformation for the coupled modified Korteweg-de Vries (cmKdV) equation is presented with the help of the gauge transformation between the corresponding3×3matrix spectral problems. By using the method of Darboux trans-formation the explicit soliton solutions of the cmKdV equation are constructed. As an application, some figures are plotted. Finally, the infinitely many conservation laws of the cmKdV equation are obtained.