Nonlinear Waves.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1988
- Accession Number
- ADA192148
Entities
People
- Athanassios S. Fokas
- Mark J. Ablowitz
Organizations
- Clarkson University