I'm not sure that what you're trying to achieve is valid, or at least optimal, with Analysis diagrams.
I'm assuming that when you say you want the boundary object to self-message, you mean that some client-side script is manipulating the UI based on user input, without engaging other portions of the system. Is that more or less correct?
If so, that's more granular than I believe the Analysis diagram is intended to function, and it's not probably very useful to a developer if you express it that way. At the same time, it's too detailed to be useful to the folks that normally participate in creating and validating Analysis diagrams. Remember that the audience for Analysis diagrams are really the customer and system analysts, working at a more functional level ("I want to do X and have the system respond by doing Y").
So, without discounting the value that this information might have to a developer, let me make some alternate suggestions on how to capture it so that it's more usable at a detailed level:
- If you want to note a general business rule or other behavioral characteristic, you may express it in the body of the Use Case that invokes the UI.
- Or perhaps as a Note in a low-fidelity mockup of the UI, if a simple explanation would make the intent obvious. See EA's Custom toolbox, or use another tool like Visio for creating the mockups.
- If there's some tricky or non-obvious logic happening within the UI that needs to be captured, you might consider using an Activity diagram to express it (careful though, since that's now defunct in UML 2.0). You could even divide it up into swimlanes to show division of responsibility between the browser (IE) and client-side objects that you create at runtime (e.g. objListFormatter, or something).
- If the logic involves non-trivial interactions between multiple run-time objects, you may even consider a Sequence diagram, but I think may be taking it kind of far. If you have that many objects interacting within the UI it's likely that you have some business logic embedded in your UI that ought to be somewhere else.