How to find people who do similar research?
MathSciNet is a pretty powerful tool for finding things in math, and some parts of applied math (from the question, I think it cover your areas).  (There's also Zentralblatt--I'm less familiar with that, but I think MSN will have more relevant tools for you.)  See about getting access to that as a guest at a local university.  

Then here are some things you can do:


Starting with papers you know that are close to your area, look them up in MathSciNet and look at the papers citing them or citing their reviews (of course you can do the first with Google scholar also, for papers that are available online).  Read the reviews to see if they are of interest.  For the ones that look interesting, repeat.  You can similarly look up all publications by a given author.
You can also search in MathSciNet by Math. Subject Classification codes to look for papers in certain subareas of applied math.
Without MathSciNet access, you can search for things on the arXiv or Google Scholar with keywords/authors/etc.  I guess this is what you have been doing.  Note, unlike Google Scholar, arXiv has subject classifications and anyone can read any paper listed there.
The subject has probably advanced a lot in 50-60 years, so it's may not be strange if most of the stuff going on now doesn't seem (at least on the surface) too close to the papers you were reading from the '50s and '60s.  So you might try looking for and reading some survey papers/lecture notes/textbooks to get a better sense of the area first.
If possible, try going to some conferences/local seminars and talking to people.