6533b85ffe1ef96bd12c18f8
RESEARCH PRODUCT
Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation
Pierre Gaillardsubject
Nonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Mathematics::Spectral Theorydescription
We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tends to points, to get solutions to the KdV equation given in terms of Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, Fredholm determinants and wronskians. This gives the bridge between the algebro-geometric approach and the Darboux dressing method.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-08-27 |