Fordy, Allan P.; Harris, Simon Nonlinear evolution equations and their stationary reductions. (English. Russian original) Zbl 0941.37051 J. Math. Sci., New York 94, No. 4, 1600-1610 (1999); translation from Zap. Nauchn. Semin. POMI 235, 245-259 (1996). This note is devoted to the relationship between an integrable nonlinear evolution equation (PDE) and its stationary flow. The authors are interested in the reduction of the infinite dimensional Hamiltonian structures to their finite dimensional counterparts. They give a systematic construction of \(x-t\) reversed equations and their Hamiltonian properties, using their isospectral properties. Reviewer: Messoud Efendiev (Berlin) MSC: 37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems Keywords:integrable nonlinear evolution equation; stationary flow; infinite dimensional Hamiltonian structures Citations:Zbl 0924.00015 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] M. Antonowicz and M. Blaszak, ”On a non-standard Hamiltonian description of NLEE,” in:Nonlinear Evolution Equations and Dynamical Systems, S. Carillo, O. Ragnisco (eds.), Springer, Berlin (1990), pp. 152–156. [2] M. Antonowicz and A. P. Fordy, ”Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems,”Comm. Math. Phys.,124, 465–86 (1989). · Zbl 0696.35172 · doi:10.1007/BF01219659 [3] M. Antonowicz and A. P. Fordy, ”Hamiltonian structures of nonlinear evolution equations,”Fordy, 273–312. · Zbl 0726.35103 [4] M. Antonowicz, A. P. Fordy, and S. Wojciechowski, ”Integrable stationary flows: Miura maps and bi-Hamiltonian structures”Phys. Letts. A,124, 143–50 (1987). · doi:10.1016/0375-9601(87)90241-6 [5] O. I. Bogoyavlenskii and S. P. Novikov, ”The relationship between Hamiltonian formalisms of stationary and nonstationary problems.” This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.