What Is Integrability?
By: edited by Vladimir E. Zakharov
Series: Springer Series in Nonlinear Dynamics, 0940-2535; Springer series in nonlinear dynamics
Publisher: Springer Berlin Heidelberg
Published: 1991
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 321
ISBN-13: 9783642887031
Subjects: Physics
Description: This monograph deals with integrable dynamic systems with an infinite number of degrees of freedom. Leading scientists were invited to discuss the notion of integrability with two main points in mind: 1. a presentation of the various recently elaborated methods for determining whether a given system is integrable or not; 2. to understand the increasingly more important role of integrable systems in modern applied mathematics and theoretical physics. Topics dealt with include: the applicability and integrability of "universal" nonlinear wave models (Calogero); perturbation theory for translational invariant nonlinear Hamiltonian systems (in 2+1d) with an additional integral of motion (Zakharov, Schulman); the role of the Painlevé test for ordinary (Ercolani, Siggia) and partial differential (Newell, Tabor) equations; the theory of integrable maps in a plane (Veselov); and the theory of the KdV equation with non-vanishing boundary conditions at infinity (Marchenko).