If you are saying your Java program was stand alone (not a Java agent within Notes) and it has worked fine in a JVM on Windows, there are very good chances that it will work in JVM of Solaris.
Having said that, you also need to have Notes client/Domino installed on your Solaris machine.
From Designer help:
Run-time requirements
A computer running a Java application that makes local Domino calls must contain Domino Server, Domino Designer, or Notes Client, and must include Notes.jar in the classpath.
A computer running a Java application that makes remote Domino calls need not contain Domino or Notes, but must contain one of the NCSO archives and must include it in the classpath.
A computer running a Domino agent that makes Domino calls must include Notes.jar in the classpath.
A computer running an applet that makes Domino calls needs no Domino software or classpath assignments. The applet must be loaded from a computer containing a Domino server.