Geodesic
Overturning solitons in new two-dimensional integrable equations
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 245-259.

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Two two-dimensional nonlinear equations are constructed which are integrable by means of a one-dimensional inverse scattering problem. Soliton and $N$-soliton solutions are indicated which are smooth in one coordinate and in the other possess the same overturning property as the classical Riemann wave. Bibliography: 9 titles. 
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O. I. Bogoyavlenskii. Overturning solitons in new two-dimensional integrable equations. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 245-259. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a1/

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