Accession Number : ADA192148

Title :   Nonlinear Waves.

Descriptive Note : Final rept.,

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

Personal Author(s) : Ablowitz, Mark J ; Fokas, Athanassios S

PDF Url : ADA192148

Report Date : Feb 1988

Pagination or Media Count : 7

Abstract : This work has important applications in fluid dynamics (e.g. long waves in stratified fluids, solitons generated by ships), nonlinear optics (e.g. self-induced transparence, and self-focussing of light), digital communications via solitons, inverse scattering in one and higher dimensions. Areas of Study Include: Solutions of nonlinear multidimensional systems; arising in Physics; inverse problems, especially in multidimensions; and DBAR methodololgy; Riemann-Hilbert boundary value problems; and inverse problems; Solitons in multidimensional systems, solitons, generated by ships in narrow channels; Nonlinear systems with external focussing; Semi infinite boundary value problems; IST for nonlinear singular integro-differential equations; the Benjamin-Ono equation, the intermediate Long Wave Equation, the Sine-Hilbert equation, multidimensional generalizations; Discrete IST and numerical simulations; Painleve equations; Focussing singularities in nonlinear wave propagation; Applications to surface waves, internal waves, shear flows; nonlinear optics, S.I.T., relativity etc; Direct linearizing methods for nonlinear evolution equations; Multidimensional generalizations of the Sine-Gordon and wave equations arising in differential geometry; Algebraic methods and symmetries of multidimensional nonlinear evolution equations; and Solutions to semiperiodic multidimensional equations.

Descriptors :   *NONLINEAR SYSTEMS, *WAVE EQUATIONS, ALGEBRA, BOUNDARY VALUE PROBLEMS, CHANNELS, DIFFERENTIAL GEOMETRY, DIGITAL COMMUNICATIONS, EVOLUTION(GENERAL), EXTERNAL, FLOW, FLUID DYNAMICS, FLUIDS, FOCUSING, INTEGRAL EQUATIONS, INTERNAL WAVES, INVERSE SCATTERING, INVERSION, LONG WAVELENGTHS, NONLINEAR ALGEBRAIC EQUATIONS, NONLINEAR DIFFERENTIAL EQUATIONS, NONLINEAR PROPAGATION ANALYSIS, NUMERICAL ANALYSIS, OPTICS, SHEAR PROPERTIES, SHIPS, STRATIFICATION, SURFACE WAVES, TRANSPARENCE, WAVE PROPAGATION, WAVES

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE