There may be more Tomcats on Linux than on Windows. You can install one of 2 ways. The generic way is to download the tarball and untar it to a suitable directory (often /usr/local, but the preference seems to be /var these days). For an RPM-based system (like RedHat), download the RPM and install in the normal way. CAUTION: someone set the default ports different on the RPM distribution. Also there are no sample apps installed with the RPM, so it won't do anything until you add apps of your own.
An IDE is no substitute for an Intelligent Developer.