Abstract:
We prove the property of meromorphic extendability for every local holomorphic solution of a system of nonlinear nonautonomous ordinary differential equations. This system is a vector generalization of Painlevé's 34 equation (which is in its turn equivalent to the second Painlevé equation) and coincides with the stationary part of the symmetry of the Korteweg–de Vries equation obtained as the sum of the stationary parts of the classical Galilean symmetry and $N$ negative symmetries of this integrable evolutionary equation.
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