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. selfinduced transparence, and selffocussing 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; RiemannHilbert 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 integrodifferential equations; the BenjaminOno equation, the intermediate Long Wave Equation, the SineHilbert 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 SineGordon and wave equations arising in differential geometry; Algebraic methods and symmetries of multidimensional nonlinear evolution equations; and Solutions to semiperiodic multidimensional equations.
 Publication:

Final Report Clarkson Univ
 Pub Date:
 February 1988
 Bibcode:
 1988cupn.rept.....A
 Keywords:

 Long Wave Radiation;
 Boundary Value Problems;
 Fluid Dynamics;
 Nonlinear Evolution Equations;
 Nonlinear Optics;
 Wave Equations;
 Wave Propagation;
 Algebra;
 Differential Equations;
 Differential Geometry;
 Integral Equations;
 Internal Waves;
 Inverse Scattering;
 Shear Flow;
 Stratification;
 Surface Waves;
 Transparence;
 Fluid Mechanics and Heat Transfer