The KDV Hierarchy and Associated Trace Formulas

Abstract

Abstract. A natural algebraic approach to the KdV hierarchy and its algebro-geometric finite-gap solutions is developed. In addition, a new derivation of associated higher-order trace formulas in connection with one-dimensional Schrödinger operators is presented.

A Class of Matrix-valued Schrödinger Operators with Prescribed Finite-band Spectra

“…An analysis of the recursion relation (2.49) for M ±,k combined with (5.7), (5.11) then proves that R k is of the form [28], [31], [36], [38], [50], [67]). …”

Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy’s 60th Birthday

“…For further information on these circle of ideas see [16,17,37,44,45,46,47,50,51,52,53,55,59,69,107,111,112,113,124,132,145]. In particular, we mention also the review by Fritz [38].…”

Darboux-type transformations and hyperelliptic curves

“…Lemma 2.1. (see, e.g., [30], [32]) Suppose f n+1,x (x) = 0 and let P = (z, y) ∈ K n \{P ∞ }, x, x 0 ∈ C. Then φ(P, x) satisfies the Riccati-type equation W (ψ(P, · , x 0 ), ψ(P * , · , x 0 )) = −2iy(P )/F n (z, x 0 ), (2.31)…”