Open AccessExistence and uniqueness of analytic solutions of the Shabat equation
Author(s) -
Eugenia N. Petropoulou
Publication year - 2005
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/aaa.2005.855
Subject(s) - algorithm , uniqueness , mathematics , mathematical analysis
Sufficient conditions are given so that the initial value problemfor the Shabat equation has a unique analytic solution, which,together with its first derivative, converges absolutely for z∈ℂ:|z|0. Moreover, a bound of this solutionis given. The sufficient conditions involve only the initialcondition, the parameters of the equation, and T. Furthermore,from these conditions, one can obtain an upper bound for T. Ourresults are in consistence with some recently found results
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