Geodesic
The Cauchy problem for Whitham equation.~I
Matematičeskoe modelirovanie, Tome 2 (1990) no. 9, pp. 70-87.

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The Cauchy problem for the nonlinear nonlocal Whitham equation is considered. The local in time existence, the large time existence and the smoothing of discontinious initial data are studied. 
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     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {The {Cauchy} problem for {Whitham} {equation.~I}},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     volume = {2},
     number = {9},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_9_a6/}
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P. I. Naumkin; I. A. Shishmarev. The Cauchy problem for Whitham equation.~I. Matematičeskoe modelirovanie, Tome 2 (1990) no. 9, pp. 70-87. http://geodesic.mathdoc.fr/item/MM_1990_2_9_a6/