Accession Number : ADA192988

Title :   Inverse Problems and a Unified Approach to Integrability in 1, 1+1 and 2+1 Dimensions,

Corporate Author : CLARKSON UNIV POTSDAM NY DEPT OF MATHEMATICS AND COMPUTER SCIENCE

Personal Author(s) : Fokas, A S ; Papageorgiou, V

PDF Url : ADA192988

Report Date : Jan 1986

Pagination or Media Count : 25

Abstract : This paper emphasizes that there exists a unified approach for solving initial value problems for equations in 1, 1+1 (i.e., one spatial and one temporal), and 2+1 (i.e., two spatial and one temporal) dimensions. Furthermore it remarks on inverse problems in higher than two spatial dimensions. Although these inverse problems are not related to physically significant nonlinear evolution equations, they are useful in the context of inverse scattering. In this presentation we emphasize the main ideas. The detail formalisms can be found in the cited papers. It turns out that solving the initial value problem for some equations for q(t), or q(x,t), or q(x,y,t) is equivalent to solving an inverse problem for some related eigenfunction psi(z; t), or psi(z; x, t), or psi(z; x, y, t). The inverse problem takes the form of a Riemann-Hilbert (RH) problem for equations in 1 and 1+1, and the form of a nonlocal RH problem or of a (DBAR) problem for equations in 2+1 (a DBAR problem is generalization of a RH problem).

Descriptors :   *INVERSION, *BOUNDARY VALUE PROBLEMS, EVOLUTION(GENERAL), INVERSE SCATTERING, NONLINEAR ALGEBRAIC EQUATIONS, PROBLEM SOLVING

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE