Existence and uniqueness of analytic solutions of the Shabat equation
Petropoulou, Eugenia N.
Abstr. Appl. Anal., Tome 2005 (2005) no. 2, p. 855-862 / Harvested from Project Euclid
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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 $z\in\mathbb{C}:|z| \lt T$ , $T \gt 0$ . Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and $T$ . Furthermore, from these conditions, one can obtain an upper bound for $T$ . Our results are in consistence with some recently found results.
Publié le : 2005-10-16
Classification:  
@article{1135272158,
     author = {Petropoulou, Eugenia N.},
     title = {Existence and uniqueness of analytic solutions of the Shabat equation},
     journal = {Abstr. Appl. Anal.},
     volume = {2005},
     number = {2},
     year = {2005},
     pages = { 855-862},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1135272158}
}

Petropoulou, Eugenia N. Existence and uniqueness of analytic solutions of the Shabat equation. Abstr. Appl. Anal., Tome 2005 (2005) no. 2, pp.  855-862. http://gdmltest.u-ga.fr/item/1135272158/