Darboux Transformation Of A Soliton Equation Associated With A 3×3 Matrix Spectral Problem

The study of the Darboux transformation for a soliton equation associated with a 3×3 matrix spectral problem is the main work of this thesis. First, beginning with the Lax pair of the soliton equation, the Darboux transformation is constructed. Depending on seed solutions u=v=w=0, explicit solutions of the equation are obtained with the help of the derived Darboux transformation. Moreover, the figures are drawn through the Mathematica. Finally, the infinite conservation laws of the soliton equation are obtained.