Closure of the squared Zakharov--Shabat eigenstates

Journal Article · Tue Jun 01 04:00:00 EDT 1976 · J. Math. Anal. Appl.; (United States)

DOI:https://doi.org/10.1016/0022-247X(76)90201-8· OSTI ID:7347267

Kaup, D J

By solution of the inverse scattering problem for a third-order (degenerate) eigenvalue problem, the closure of the squared eigenfunctions of the Zakharov--Shabat equations is found. The question of the completeness of squared eigenstates occurs in many aspects of ''inverse scattering transforms'' (solving nonlinear evolution equations exactly by inverse scattering techniques), as well as in various aspects of the inverse scattering problem. The method used here is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and the strong analogy between these results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix is pointed out.

• Research Organization: Clarkson Coll. of Tech., Postdam, NY
• OSTI ID: 7347267
• Journal Information: J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 54:3; ISSN JMANA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
EIGENFUNCTIONS
EIGENSTATES
EIGENVECTORS
FUNCTIONS
INVERSE SCATTERING PROBLEM
MATRICES