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The approach to isospectral Hamiltonian flow introduced in part I is further developed to include integration of flows with singular spectral curves. The flow on finite dimensional AdViagramelbourne -invariant Poisson submanifolds of the dual of the positive part of the loop algebra is obtained through a generalization of the standard method of linearization on the Jacobi variety of the invariant spectral curve S . These curves are embedded in the total space of a line bundle T → P 1 ( C ), allowing an explicit analysis of singularities arising from the structure of the image of a moment map $$\tilde J_r :M_{N,r} \times M_{N,r} \to (\widetilde{gl}(r)^ + )*$$ from the space of rank- r deformations of a fixed N×N matrix A . https://www.viagramelbourne.nu It is shown how the linear… flow of line bundles $$E_t \to \tilde S$$ over a suitably desingularized curve $$\tilde S$$ may be used to determine both the flow of matricial polynomials L (λ) and the Hamiltonian flow in the space M N,r ×M N,r in terms of θ-functions. https://en.wikipedia.org/wiki/Sildenafil The resulting flows are proved to be completely integrable. The reductions to subalgebras developed in part I are shown to correspond to invariance of the spectral curves and line bundles $$E_t \to \tilde S$$ under certain linear or anti-linear involutions. Buy Viagra Perth The integration of two examples from part I is given to illustrate the method: the Rosochatius system, and the CNLS (coupled non-linear Schrödinger) equation.

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