6533b857fe1ef96bd12b4e78
RESEARCH PRODUCT
30 years of finite-gap integration theory
V. B. Matveevsubject
Spectral theoryGeneral MathematicsRiemann surfaceMathematical analysisGeneral EngineeringGeneral Physics and AstronomyTheta functionAlgebraic geometryInverse problemAlgebraRiemann hypothesissymbols.namesakesymbolsKorteweg–de Vries equationDifferential (mathematics)Mathematicsdescription
The method of finite-gap integration was created to solve the periodic KdV initial problem. Its development during last 30 years, combining the spectral theory of differential and difference operators with periodic coefficients, the algebraic geometry of compact Riemann surfaces and their Jacobians, the Riemann theta functions and inverse problems, had a strong impact on the evolution of modern mathematics and theoretical physics. This article explains some of the principal historical points in the creation of this method during the period 1973–1976, and briefly comments on its evolution during the last 30 years.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-06-26 | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |