Gopu, you need two things. First install a Sun JDK (the latest 1.6 or 1.5 will work fine). The JDK that comes with most Linux distro's is not up to running web servers. Though this is changing - the Open JVM that comes with the latest Ubuntu distro should work just fine. Once installed, set JAVA_HOME to where it was installed.
Second, download the latest version of Tomcat (or even the version you are running on the other system) from the Tomcat download site. Unpack it where you like (I put mine in /opt, but you can put it anywhere).
Then you are all ready to do.
One more thing - when it comes to
Java apps like Tomcat, the question of compatibility with an operating system is actually what JVM will run on the operating system, and then which version of the Java app will run on that JVM.