Darboux Transformation and Exact Solution for Novikov Equation

In this paper, the lax pair of Novikov equation is given in 3 \(\times \) 3 matrices form. Based on the spectral problem and the lax pair of Novikov equation, we construct the Darboux transformation and give the theoretical proof. By selecting the appropriate seed solution and using the obtained Darboux transformation, we can acquire the new exact solution of this equation. Finally, three-dimensional distribution and density plots of the new solution are shown. Exact solutions are depend on the different chosen seed solutions.