I have a complete code written in Visual Studio which I have ported to monodevelop in Ubuntu 14 LTS. I was thinking if there is a way to install the Sql localDB instance in Ubuntu 14.
I believe there is no way to do that. Even with Wine I don't think it will work. However, you can run your application on Ubuntu and install DB Server on another Windows computer. That should work. You could even install DB in virtual machine within your Ubuntu. Here you can find some more information on the topic: http://www.howtogeek.com/133515/4-ways-to-run-windows-software-on-linux/