To find more information about who owns an IP address you can:
- use the traceroute (unix) / tracert (windows) command line tool to find out which routers are between them and you.
- check a GeoIP database to get a very approximate geographical location of that IP address block.
- use the ripe database to check to whom the IP address block is registred, which will usually lead you to their ISP.
The exact identity is only known to the ISP which will usually only reveal it when they get a court order or similar official request from law enforcement, which requires that you report it and that they find the case relevant enough to act. Unless you actually lost data or have other tangible damages, they are unlikely to act, though.
Also, when the attacker knows what they are doing, they will use various anonymization tools to hide their identity. There are various methods to make deanonymization of internet users very difficult (which are explained in greater detail in lots of other questions on this site, so I won't go into further detail). Following the IP will likely lead you to just some hapless internet user who got his machine infected with a botnet trojan.
But acting after an attack is really not what you should be worrying about. What you should be worrying about is making sure that such attacks won't work on your systems.
Scans like that happen all the time. When you put a webserver online it usually only takes minutes until people start hammering it with all kinds of exploits. If you aren't confident in your security, you shouldn't be doing this.