On holomorphic solutions of equations of Korteweg–de Vries type

Domrin, A.

doi:10.1090/S0077-1554-2013-00206-X

On holomorphic solutions of equations of Korteweg–de Vries type
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by A. V. Domrin
Translated by: V. E. Nazaikinskii

Trans. Moscow Math. Soc. 2012, 193-206

DOI: https://doi.org/10.1090/S0077-1554-2013-00206-X

Published electronically: March 21, 2013

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Abstract:

We show that, for any of the equations indicated in the title, every solution locally holomorphic in $x$ and $t$ admits global meromorphic continuation in $x$ for each $t$ with trivial monodromy at each pole. By way of application, we describe all possible envelops of meromorphy of local holomorphic solutions of the Boussinesq equation.

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