168 citations · 614 across the 54 of their papers we have counts for
6 papers · 1 filter
Darboux-type transformations and hyperelliptic curves
Fritz Gesztesy, Helge Holden
We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebr…
The classical Boussinesq hierarchy revisited
Fritz Gesztesy, Helge Holden
We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBs…
The Cole-Hopf and Miura transformations revisited
Fritz Gesztesy, Helge Holden
An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations…
Dubrovin equations and integrable systems on hyperelliptic curves
F. Gesztesy, H. Holden
We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the correspond…
A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
Fritz Gesztesy, Helge Holden
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to ot…
Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
W. Bulla, F. Gesztesy, H. Holden +1
Combining algebro-geometric methods and factorization techniques for finite difference expressions we provide a complete and self-contained treatment of all real-valued quasi-perio…