Thanks for your answer.
As you suggested,I registered my SSL certificate, with is signed by GeoTrust, but I get always the message "Accept unknown certificate ? the server certificate is not signed by a trusted certificate authority". Surprising message, because the certificate is trusted !
The good point is: now, I haven't to re-accept the certificate, from the android application, each time I reboot my smartphone: now, the chat user stays connected after reboot.
Before, with the self signed certificate, after reboot, the chat user was disconnected. I had to re-accept the certificate at each reboot, and that's why I wanted to put a certificate signed by trusted authority.
If you have an idea why the trusted certificate is considered not trusted ...
Thanks. Best regards