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.


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