Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for , . Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and . Furthermore, from these conditions, one can obtain an upper bound for . Our results are in consistence with some recently found results.
"Existence and uniqueness of analytic solutions of the Shabat equation." Abstr. Appl. Anal. 2005 (8) 855 - 862, 16 October 2005. https://doi.org/10.1155/AAA.2005.855