Negative Volterra Flows and Mixed Volterra Flows and Their Infinitely Many Conservation Laws

摘要

In this article, by means of considering an isospectral operator equationwhich corresponds to the Volterra lattice, and constructing opportune timeevolution problems with negative powers of spectral parameter, and usingdiscrete zero curvature representation, negative Volterra flows are proposed.We also propose the mixed Volterra flows, which come from positive and negativevolterra flows. From the Lax representation, we demonstrate the existence ofinfinitely many conservation laws for the two flows and give the correspondingconserved densities and the associated fluxes formulaically. Thus theirintegrability is further confirmed.