TY - JOUR

T1 - Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schrödinger spectral problem

AU - Zhu, Zuo Nong

AU - TAM, Hon Wah

AU - Ding, Qing

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2003/4/21

Y1 - 2003/4/21

N2 - In this Letter, by means of considering matrix form of a new Schrödinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples.

AB - In this Letter, by means of considering matrix form of a new Schrödinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples.

UR - http://www.scopus.com/inward/record.url?scp=0037459908&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(03)00350-5

DO - 10.1016/S0375-9601(03)00350-5

M3 - Article

AN - SCOPUS:0037459908

SN - 0375-9601

VL - 310

SP - 281

EP - 294

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4

ER -