A special addition theorem for theta-functions and nonlinear equations
In the article under review, the authors derive some consequences from the Mumford theorem characterizing the Jacobi varieties of hyperelliptic algebraic curves in terms of theta-constants. These formulas, treated as special addition theorems for the corresponding theta-functions, are applied to effectivization of theta-functional formulas for finite gap solutions to the Korteweg-de Vries and sine-Gordon equations.
scientific article; zbMATH DE number 1286057