KdV hierarchy via Abelian coverings and operator identities
| Autor: | Benjamin Eichinger, Tom VandenBoom, Peter Yuditskii |
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| Rok vydání: | 2019 |
| Předmět: |
37K10
37K15 35Q53 34L40 Pure mathematics Mathematics::Analysis of PDEs FOS: Physical sciences Boundary (topology) KdV hierarchy 01 natural sciences Mathematics - Spectral Theory symbols.namesake 0103 physical sciences FOS: Mathematics Initial value problem 0101 mathematics Abelian group Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Spectral Theory (math.SP) Mathematical Physics Mathematics Hierarchy (mathematics) Riemann surface 010102 general mathematics Mathematical Physics (math-ph) General Medicine Function (mathematics) Mathematics::Spectral Theory Nonlinear Sciences::Exactly Solvable and Integrable Systems symbols 010307 mathematical physics |
| Zdroj: | Transactions of the American Mathematical Society, Series B. 6:1-44 |
| ISSN: | 2330-0000 |
| Popis: | We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with $V$ as an initial value. More generally, 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. Comment: 52 pages, 1 figure |
| Databáze: | OpenAIRE |
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