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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - KDV HIERARCHY VIA ABELIAN COVERINGS AND OPERATOR IDENTITIES
AU - Eichinger, B.
AU - Vandenboom, T.
AU - Yuditskii, P.
N1 - Publisher Copyright: © 2019 by the authors under.
PY - 2019/1/2
Y1 - 2019/1/2
N2 - We establish precise spectral criteria for potential functions V of reflectionless Schrödinger operators LV = −∂x2 + V to admit solutions to the Korteweg–de Vries (KdV) hierarchy with V as an initial value. More gener-ally, our methods extend the classical study of algebro-geometric solutions for the KdV hierarchy to noncompact Riemann surfaces by defining generalized Abelian integrals and analogues of the Baker-Akhiezer function on infinitely connected domains with a uniformly thick boundary satisfying a fractional moment condition.
AB - We establish precise spectral criteria for potential functions V of reflectionless Schrödinger operators LV = −∂x2 + V to admit solutions to the Korteweg–de Vries (KdV) hierarchy with V as an initial value. More gener-ally, our methods extend the classical study of algebro-geometric solutions for the KdV hierarchy to noncompact Riemann surfaces by defining generalized Abelian integrals and analogues of the Baker-Akhiezer function on infinitely connected domains with a uniformly thick boundary satisfying a fractional moment condition.
U2 - 10.1090/btran/30
DO - 10.1090/btran/30
M3 - Journal article
AN - SCOPUS:85082851725
VL - 6
SP - 1
EP - 44
JO - Transactions of the American Mathematical Society Series B
JF - Transactions of the American Mathematical Society Series B
SN - 2330-0000
ER -