About solving research papers involving complex Mathematics Throughout my Ph.D., I have had difficulty in solving (maths in) research paper from other researchers. After the basic few steps, the researchers assume either one thing or the other thing, or have a complex integral or derivate (or any other) format and then come up with the solution that is entirely unknown to me. Sometimes after rigorous effort, I find the way authors solve. But mostly, I assume what they did is right and then carry on (which is not the right way).

How do other researchers (students) deal with this issue?

PS. I am from wireless telecommunication background
I would start with e-mailing the authors, or perhaps other experts in your area that you are close to and asking for help from them. I've found that a lot of researchers, even big names, are happy to discuss details about their work (or at least they seem to respond to questions of this nature more frequently than you would expect).

Keep in mind however, that in some fields of physics and engineering (I am not sure if this is true of yours) mathematical rigor isn't a high priority, and so it can be impossible to verify the mathematical reasoning in the paper, even for expert mathematicians working in your area. As a mathematician I find this frustrating, but my understanding is that researchers in physics/engineering are more concerned with the big-picture ideas than making sure all the mathematical details are correct, and perhaps you can take that attitude too.

As an example, my collaborators and I were trying to understand this physics paper (from a top physics journal, written by a distinguished physicist), and we found it impossible to understand the mathematics- there was a step in the calculation where they had an infinite sum that clearly diverged! We emailed the author, and he acknowledged that the sum diverged and the calculations in the paper were not correct, but the idea was still valid. This is a fairly typical point of view in physics and engineering from my experience. So it might be good to adjust your expectations on to what extent you can recreate the mathematics in a physics or engineering paper.