The inverse spectral method for periodic soliton equations was analyzed and developed for numerical implementation. It was then used to describe shock waves in a one-dimensional discrete medium and spatial chaos in a non-linear partial differential equation. Algebraic and geometric symmetries of soliton equations were studied. Pattern formation and the transition to turbulence in Rayleigh-Benard convection were investigated; a new modulational theory describes 'imperfections' in convection roll patterns. Finally, infinite- dimensional maps associated with bistability in an optical ring cavity were studied, and basic fixed points and first bifurcations were analyzed. Topics discussed were: Solvable models of mathematical physics; Spatial coherence and temporal chaos; Convection in large aspect ratio systems; and Transition to turbulence; and additional keywords: Painleve equations.
Final rept. 1981-1984
25 MAY 84
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