Abstract and Applied Analysis
Volume 2005 (2005), Issue 8, Pages 855-862
Existence and uniqueness of analytic solutions of the Shabat equation
Division of Applied Mathematics and Mechanics, Mechanics, Department of Engineering Sciences, School of Engineering, University of Patras, Patras 26500, Greece
Received 30 May 2004
Copyright © 2005 Eugenia N. Petropoulou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.