I'm not really sure where to post this question, but because I'm a newbie I'll just post it here....
I've created a website with a series of custom search engines (e.g. cseA, cseB, cseC, cseD). In many cases a user will want to search the same keyword in more than one of the search engines (but they should not be combined). Right now if a user searches "keyword" in cseA and then wants to search "keyword" in cseB then the user has to click my link to go to the cseB homepage and then retype "keyword". I'd like to set it up so that once "keyword" is searched in cseA, if the user wants to search it in cseB then the user clicks the link for cseB and "keyword" is immediately searched.
I know this is a little confusing so I'll give an example: In google if one searches "london" for the general web search and then on the results page clicks "images" then one is immediately taken to an image search of "london", rather than the google images homepage. This is what I'm looking to achieve.