N-fold Darboux transformation and conservation laws of the modified Volterra lattice

Abstract

In this work, we study the modified Volterra lattice. Applying the gauge transformation of the associated [Formula: see text] matrix spectral problems, we establish the N-fold Darboux transformation (DT), and then construct a few explicit solutions in terms of determinants upon using the obtained DT. Moreover, all the results are illustrated by the graphs of the solitonic evolution profiles of the aforementioned solutions. Finally, infinitely many conservation laws for the modified Volterra lattice are proposed. The obtained results of this research might be applied to the research on nonlinear phenomena in physics or engineering areas.