Geodesic
Liouville's theorem and the inverse scattering method
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 113-125

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On the base of Liouville's theorem, an approach to the integration of the Zakharov–Shabat equations is developed. It arises as a synthesis of ideas of the “finite-gape” integration, the matrix Riemann problem method and the theory of isomonodromic deformations. With the help of this scheme the “dressing procedure” for the Bullough–Dodd equation is obtained. 
@article{ZNSL_1984_133_a7,
     author = {A. R. Its},
     title = {Liouville's theorem and the inverse scattering method},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--125},
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     volume = {133},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a7/}
}
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A. R. Its. Liouville's theorem and the inverse scattering method. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 113-125. http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a7/