Geodesic
A periodic problem for Whitham's equation
Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 403-426

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A periodic problem for the nonlinear and nonlocal Whitham equation is studied. Questions of the breakdown of a solution in finite time, the existence of a solution globally in time, and the smoothing of a discontinuous initial perturbation are considered. The asymptotics of a solution with respect to the smallness of the interaction is found. Bibliography: 10 titles. 
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     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {A periodic problem for {Whitham's} equation},
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     year = {1990},
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     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/}
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P. I. Naumkin; I. A. Shishmarev. A periodic problem for Whitham's equation. Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 403-426. http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/