Geodesic
Existence of a global solution of the Whitham equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 58-71

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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 $1\leq N\in\mathbf N$. 
@article{TMF_2000_122_1_a5,
     author = {T. Grava},
     title = {Existence of a global solution of the {Whitham} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {58--71},
     publisher = {mathdoc},
     volume = {122},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a5/}
}
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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/