scholarly journals Reflectionless potentials for an ordinary differential operator of order four

2006 ◽  
Vol 22 (1) ◽  
pp. 135-153 ◽  
Author(s):  
A Laptev ◽  
R Shterenberg ◽  
V Sukhanov ◽  
J Östensson
Keyword(s):  
Differential Operator ◽  
Ordinary Differential Operator ◽  
Order Four

A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†

1978 ◽  
Vol 82 (1-2) ◽  
pp. 117-134 ◽  
Author(s):  
Richard C. Gilbert
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Asymptotic Expansions ◽  
Differential Operators ◽  
Ordinary Differential Operator ◽  
Ordinary Differential Operators ◽  
Half Axis ◽  
Complex Coefficients

SynopsisFormulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.

scholarly journals Spectral Curve of the Halphen Operator

2016 ◽  
Vol 60 (2) ◽  
pp. 451-460
Author(s):  
Andrey E. Mironov ◽  
Dafeng Zuo
Keyword(s):  
Differential Operator ◽  
Spectral Curve ◽  
Ordinary Differential Operator ◽  
Order Operator ◽  
Third Order ◽  
Image Position

AbstractThe Halphen operator is a third-order operator of the formwhere g ≠ 2 mod(3), where the Weierstrass ℘-function satisfies the equationIn the equianharmonic case, i.e. g2 = 0, the Halphen operator commutes with some ordinary differential operator Ln of order n ≠ 0 mod(3). In this paper we find the spectral curve of the pair L3, Ln.

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