TY - JOUR
T1 - The Korteweg-de Vries hierarchy of isospectral transformations
T2 - Towards a general explicit expression
AU - Rosenhouse, Avia
AU - Katriel, Jacob
PY - 1987
Y1 - 1987
N2 - The structure of the Korteweg-de Vries hierarchy of evolution equations, generating isospectral transformations, is elucidated by means of a study of its recurrence relations. For the mth member of the KdV hierarchy, which can be written in the form Vt = -2Am+1,x, where the Ai satisfy the recurrence relation Am+1,x = VAm,x + 1/2AmVx - 1/4Am,xxx, it is shown that A m is a homogeneous polynomial in ∂i V/∂x i. A general combinatorial formula for the coefficients of all the monomials entering Am, up to a set of constants determined by means of a recurrence relation, is derived.
AB - The structure of the Korteweg-de Vries hierarchy of evolution equations, generating isospectral transformations, is elucidated by means of a study of its recurrence relations. For the mth member of the KdV hierarchy, which can be written in the form Vt = -2Am+1,x, where the Ai satisfy the recurrence relation Am+1,x = VAm,x + 1/2AmVx - 1/4Am,xxx, it is shown that A m is a homogeneous polynomial in ∂i V/∂x i. A general combinatorial formula for the coefficients of all the monomials entering Am, up to a set of constants determined by means of a recurrence relation, is derived.
UR - http://www.scopus.com/inward/record.url?scp=36549103030&partnerID=8YFLogxK
U2 - 10.1063/1.527536
DO - 10.1063/1.527536
M3 - Article
AN - SCOPUS:36549103030
SN - 0022-2488
VL - 28
SP - 1344
EP - 1350
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 6
ER -