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On holomorphic solutions of equations of Korteweg-de Vries type. (English. Russian original) Zbl 1291.35278
Trans. Mosc. Math. Soc. 2012, 193-206 (2012); translation from Tr. Mosk. Mat. O.-va 73, No. 2, 241-257 (2012).
Summary: 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.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
30B40 Analytic continuation of functions of one complex variable
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