Abstract:
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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