6533b7d3fe1ef96bd1260a39
RESEARCH PRODUCT
New degeneration of Fay's identity and its application to integrable systems
Caroline Kallasubject
Pure mathematicsIntegrable systemGeneral MathematicsMathematics::Analysis of PDEsFOS: Physical sciences01 natural sciencesIdentity (music)Mathematics - Algebraic Geometrysymbols.namesakeMathematics::Algebraic Geometry[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesFOS: MathematicsLimit (mathematics)[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]0101 mathematics010306 general physicsAlgebraic Geometry (math.AG)Nonlinear Schrödinger equationNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematicsSmoothness (probability theory)010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Mathematical Physics (math-ph)[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Nonlinear Sciences::Exactly Solvable and Integrable SystemsScheme (mathematics)symbolsPairwise comparison[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]description
In this paper, we find a new degenerated version of Fay's trisecant identity; this degeneration corresponds to the limit when the four points entering the trisecant identity coincide pairwise. This degenerated version of Fay's identity is used to construct algebro-geometric solutions to the multi-component nonlinear Schrodinger equation. This identity also leads to an independent derivation of algebro-geometric solutions to the Davey–Stewartson equations previously obtained in [17] in the framework of the Krichever scheme. We also give the condition of smoothness of the obtained solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-04-13 |