We study a certain family of Schrodinger operators whose eigenfunctions phi(x, lambda) satisfy a differential equation in the spectral parameter lambda of the form B(lambda, partial derivative-lambda)phi = THETA(x)phi. We show that the flows of a hierarchy of master symmetries for KdV are tangent to the manifolds that compose the strata of this class of bispectral potentials. This extends and complements a result of Duistermaat and Grunbaum concerning a similar property for the Adler and Moser potentials and the flows of the KdV hierarchy
Zubelli, J., Magri, F. (1991). Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 141(2), 329-351 [10.1007/BF02101509].
Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV
Magri, F
1991
Abstract
We study a certain family of Schrodinger operators whose eigenfunctions phi(x, lambda) satisfy a differential equation in the spectral parameter lambda of the form B(lambda, partial derivative-lambda)phi = THETA(x)phi. We show that the flows of a hierarchy of master symmetries for KdV are tangent to the manifolds that compose the strata of this class of bispectral potentials. This extends and complements a result of Duistermaat and Grunbaum concerning a similar property for the Adler and Moser potentials and the flows of the KdV hierarchyI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.