Geodesic
Finite-gap attractors and transition processes of the shock wave type in integrable systems
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 25-36

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For integrable nonlinear equations of KdV-type it is shown that well-known finite-gap solutions can be interpreted as finite-dimentional attractors. Some shock ware problems for these systems are discussed. 
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     author = {R. F. Bikbaev},
     title = {Finite-gap attractors and transition processes of the shock wave type in integrable systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {25--36},
     publisher = {mathdoc},
     volume = {199},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a1/}
}
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R. F. Bikbaev. Finite-gap attractors and transition processes of the shock wave type in integrable systems. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 25-36. http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a1/