Darboux transformation and conservation laws of a integrable evolution equations with 3 × 3 Lax pairs

Darboux transformation for a nonlinear integrable equation associated with 3 × 3 matrix spectral problems, which is constructed by Lenells, is derived with the aid of the gauge transformation between the corresponding Lax pairs. By using the Darboux transformation, new explicit solutions for the nonlinear integrable equation are given and their figures are plotted. Finally, infinitely many conservation laws of this equation are deduced.