It is a pretty broad question! You can use JIRA off the shelf for Requirement Management. You just need to create a new issue type (or make use of "New Feature" type), create its own workflow, custom fields that you need etc.
Greenhopper is a good Agile Project Management plugin to manage your requirements too.
Atlassian uses JIRA to manage the requirements.
I have this same problem. I'm thinking about implementing some of the custom fields called out in the answered Stack Overflow question here:
But really, it sounds like the best solution would be to enable some of the standalone JIRA tools like RMsis or synapseRT.
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