Geodesic
Existence of a global solution of the Whitham equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 58-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Cauchy problem for Whitham equations with monotonic analytic initial data is studied. If the initial data $f(u)$ satisfies the condition $f^{(2N+1)}(u)<0$ for all $u\in\mathbf R$ except a number of isolated points, then the genus of the solution of the Whitham equations is at most equal to $N$, where $1\leq N\in\mathbf N$. 
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T. Grava. Existence of a global solution of the Whitham equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 58-71. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a5/

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