You’d be looking at a simple bit of jQuery like this (obviously you will have to change the selectors)
currentSlide = $('.slider .active');
nextSlide = currentSlide.next();
prevSlide = currentSlide.prev();
/** then to get for instance, a caption from inside the slides : *//
nextSlideData = nextSlide.find('p.caption').html();
prevSlideData = prevSlide.find('p.caption').html();
alert('Next caption: '+nextSlideData+' & Previous caption: '+prevSlideData);