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 -