Existence and uniqueness of analytic solutions of the Shabat equation
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∈ℂ:|z|<T, T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.855 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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∈ℂ:|z|<T, T>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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |