Is it possible to get next element in the Stream?

No, this is not possible using streams, at least not easily. The stream API abstracts away from the order in which the elements are processed: the stream might be processed in parallel, or in reverse order. So "the next element" and "previous element" do not exist in the stream abstraction.

You should use the API best suited for the job: stream are excellent if you need to apply some operation to all elements of a collection and you are not interested in the order. If you need to process the elements in a certain order, you have to use iterators or maybe access the list elements through indices.

I haven't see such use case with streams, so I can not say if it is possible or not. But when I need to use streams with index, I choose IntStream#range(0, table.length), and then in lambdas I get the value from this table/list.

For example

    int[] arr = {1,2,3,4};
    int result = IntStream.range(0, arr.length)
            .map(idx->idx>0 ? arr[idx] + arr[idx-1]:arr[idx])
            .sum();