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Existence and uniqueness of analytic solutions of the Shabat equation. (English) Zbl 1113.34062

The author presents sufficient conditions, so that the initial value problem for the Shabat equation has a unique analytic solution, which together with its first derivative, converges absolutely for \(z\in\mathbb{C}: |z|<T\), \(T> 0\). The basic idea of the method is the equivalent transformation of the functional differential equation under consideration into an operator equation.

MSC:

34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
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