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

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

2003-04-10

arxiv.org/abs/nlin/0304015v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero curvature representation, negative Volterra flows are proposed. We also propose the mixed Volterra flows, which come from positive and negative volterra flows. From the Lax representation, we demonstrate the existence of infinitely many conservation laws for the two flows and give the corresponding conserved densities and the associated fluxes formulaically. Thus their integrability is further confirmed.

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