TY - JOUR

T1 - Rational solutions of nonlinear evolution equations, vertex operators, and bispectrality

AU - Zubelli, Jorge P.

N1 - Funding Information:
* Research supported in part by ONR Contract NOOO14-84-C-015a9n d NSF Grant DMS 87-20007.

PY - 1992/5

Y1 - 1992/5

N2 - We prove that if q(x, t2, ..., tm) and r(x, t2, ..., tm) are certain rational solutions of the AKNS hierarchy, then there are eigenfunctions ψ(x, k) of the AKNS/ZS operator L= ∂x -q r -∂x satisfying a differential equation in the spectral parameter k of the form B(k, ∂k)ψ = Θ(x)ψ, where B(∂k, k) is a matrix differential operator, independent of x, and Θ is a nonconstant function of x. We also discuss the relation between this result and a similar one for the rational solutions of the Schrödinger operator with potentials in the manifold of rational solutions of the KdV hierarchy.

AB - We prove that if q(x, t2, ..., tm) and r(x, t2, ..., tm) are certain rational solutions of the AKNS hierarchy, then there are eigenfunctions ψ(x, k) of the AKNS/ZS operator L= ∂x -q r -∂x satisfying a differential equation in the spectral parameter k of the form B(k, ∂k)ψ = Θ(x)ψ, where B(∂k, k) is a matrix differential operator, independent of x, and Θ is a nonconstant function of x. We also discuss the relation between this result and a similar one for the rational solutions of the Schrödinger operator with potentials in the manifold of rational solutions of the KdV hierarchy.

UR - http://www.scopus.com/inward/record.url?scp=38249011909&partnerID=8YFLogxK

U2 - 10.1016/0022-0396(92)90084-Z

DO - 10.1016/0022-0396(92)90084-Z

M3 - Article

AN - SCOPUS:38249011909

SN - 0022-0396

VL - 97

SP - 71

EP - 98

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -