Two new integrable lattice hierarchies associated with a discrete Schrödinger nonisospectral problem and their infinitely many conservation laws

Zuo-Nong Zhu*, Weimin Xue

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)
8 Downloads (Pure)

Abstract

In this Letter, by means of using discrete zero curvature representation and constructing opportune time evolution problems, two new discrete integrable lattice hierarchies with n-dependent coefficients are proposed, which relate to a new discrete Schrödinger nonisospectral operator equation. The relation of the two new lattice hierarchies with the Volterra hierarchy is discussed. It has been shown that one lattice hierarchy is equivalent to the positive Volterra hierarchy with n-dependent coefficients and another lattice hierarchy with isospectral problem is equivalent to the negative Volterra hierarchy. We demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes formulaically. Thus their integrability is confirmed.

Original languageEnglish
Pages (from-to)396-407
Number of pages12
JournalPhysics Letters A
Volume320
Issue number5-6
DOIs
Publication statusPublished - 12 Jan 2004
Externally publishedYes

Scopus Subject Areas

  • Physics and Astronomy(all)

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