TY - JOUR

T1 - (1+1)-dimensional m-cKdV, g-cKdV integrable systems, and (2+1)-dimensional m-cKdV hierarchy

AU - Zhang, Yufeng

AU - TAM, Hon Wah

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2008/12

Y1 - 2008/12

N2 - A few isospectral problems are introduced by referring to that of the cKdV equation hierarchy, for which two types of integrable systems called the (1 + 1)-dimensional m-cKdV hierarchy and the g-cKdV hierarchy are generated, respectively, whose Hamiltonian structures are also discussed by employing a linear functional and the quadratic-form identity. The corresponding expanding integrable models of the (1 + 1)-dimensional m-cKdV hierarchy and g-cKdV hierarchy are obtained. The Hamiltonian structure of the latter one is given by the variational identity, proposed by Ma Wen-Xiu as well. Finally, we use a Lax pair from the self-dual Yang-Mills equations to deduce a higher dimensional m-cKdV hierarchy of evolution equations and its Hamiltonian structure. Furthermore, its expanding integrable model is produced by the use of a enlarged Lie algebra.

AB - A few isospectral problems are introduced by referring to that of the cKdV equation hierarchy, for which two types of integrable systems called the (1 + 1)-dimensional m-cKdV hierarchy and the g-cKdV hierarchy are generated, respectively, whose Hamiltonian structures are also discussed by employing a linear functional and the quadratic-form identity. The corresponding expanding integrable models of the (1 + 1)-dimensional m-cKdV hierarchy and g-cKdV hierarchy are obtained. The Hamiltonian structure of the latter one is given by the variational identity, proposed by Ma Wen-Xiu as well. Finally, we use a Lax pair from the self-dual Yang-Mills equations to deduce a higher dimensional m-cKdV hierarchy of evolution equations and its Hamiltonian structure. Furthermore, its expanding integrable model is produced by the use of a enlarged Lie algebra.

UR - http://www.scopus.com/inward/record.url?scp=58449091499&partnerID=8YFLogxK

U2 - 10.1139/P08-098

DO - 10.1139/P08-098

M3 - Article

AN - SCOPUS:58449091499

SN - 0008-4204

VL - 86

SP - 1367

EP - 1380

JO - Canadian Journal of Physics

JF - Canadian Journal of Physics

IS - 12

ER -