Geodesic
Nonlinear evolution equations and their stationary reductions
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–2, Tome 235 (1996), pp. 245-259

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In recent years there have been many papers on stationary flows of integrable nonlinear evolution equations and their Hamiltonian properties. In particular there have been some results concerning the reversal of the roles of $x$ and $t$, resulting in PDEs which are Hamiltonian and give the usual stationary Poisson brackets in the reduced case. To date the results have been rather ad hoc and disparate. In this brief report we give a systematic construction of these $x-t$ reversed equations and their Hamiltonian properties, using their isospectral properties. We illustrate our approach with examples from the KdV hierarchy. Bibl. 5 titles. 
@article{ZNSL_1996_235_a12,
     author = {Allan P. Fordy and Simon Harris},
     title = {Nonlinear evolution equations and their stationary reductions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {245--259},
     publisher = {mathdoc},
     volume = {235},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_235_a12/}
}
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Allan P. Fordy; Simon Harris. Nonlinear evolution equations and their stationary reductions. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–2, Tome 235 (1996), pp. 245-259. http://geodesic.mathdoc.fr/item/ZNSL_1996_235_a12/