Titlebook: Symmetries and Singularity Structures; Integrability and Ch Muthuswamy Lakshmanan,Muthiah Daniel Conference proceedings 1990 Springer-Verla

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Lie Algebra, Bi-Hamiltonian Structure and Reduction Problem for Integrable Nonlinear Systemssystem with 3 × 3 matrix structure. An important aspect of our formulation is to implement reduction mechanism to arrive at a specific nonlinear system. As examples we have discussed the cases of KdV, Langmuir solitons.

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On the Role of Virasoro, Kac-Moody Algebra and Conformal Invariance in Soliton Hierarchieshe importance of conformal invariance is emphasized and some new aspects of complete integrability are exhibited. Lastly the relation between bi-Hamiltonian structure and conformal invariance is explained.

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Avoided Level Crossing, Solitons and Random Matrix Theoryntegrability parameter is varied. We proceed to study the statistical mechanics of gCM system on the basis of the grand-canonical ensemble. We obtain the probability densities for both the level curvature and level spacing, thereby suggesting an important way to go beyond the traditional framework of the random matrix theory.

期满

A Singularity Analysis Approach to the Solutions of Duffing’s Equationngularity patterns are seen to further “condense”, as Q increases and the motion becomes . more chaotic in real t. These results suggest that series expansions near singularities in the complex t-plane can provide useful representations of the general solution of Duffing’s equation.

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