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RESEARCH PRODUCT
Degenerate Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation and the degenerate rational case
Pierre Gaillardsubject
KdV equationPure mathematicsGeneral Physics and AstronomyFredholm determinantTheta function01 natural sciencessymbols.namesakeWronskians[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Fredholm determinant0103 physical sciencesRiemann theta functions0101 mathematicsAbelian group010306 general physicsKorteweg–de Vries equationMathematical PhysicsMathematicsWronskianRiemann surface010102 general mathematicsDegenerate energy levelsRiemann hypothesisNonlinear Sciences::Exactly Solvable and Integrable SystemsRiemann surfacesymbolsGeometry and Topologydescription
International audience; We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tend 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.We construct also multi-parametric degenerate rational solutions of this equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-03-01 |