Geodesic
Invariant measures generated by higher conservation laws for the~Korteweg--de~Vries equations
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 803-822

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The well-posedness of the Cauchy problem that is periodic with respect to the spatial variable is proved for the Korteweg–de Vries equation. For dynamical systems generated by this equation on appropriate phase spaces the invariance of the Borel measures associated with the higher conservation laws is proved. 
@article{SM_1996_187_6_a1,
     author = {P. E. Zhidkov},
     title = {Invariant measures generated by higher conservation laws for {the~Korteweg--de~Vries} equations},
     journal = {Sbornik. Mathematics},
     pages = {803--822},
     publisher = {mathdoc},
     volume = {187},
     number = {6},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_6_a1/}
}
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P. E. Zhidkov. Invariant measures generated by higher conservation laws for the~Korteweg--de~Vries equations. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 803-822. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a1/