Where to submit an article of applied maths for physics
Remember that J. Phys. A and J. Math. Phys. are quite top journals and they reject lots of reasonable papers not because they would be off-topic but because they are "not good enough for them" (whatever that means).

IMHO, if you feel that your identities are something completely new to the world of maths, you should find a reasonably good math journal, because they are likely interesting to math people as well. On the other hand, if you feel that the results are interesting only to (theoretical/mathematical) physicists, go for a journal in this branch.

I don't know any mathematical physics journals personally.

For math journals about identities/symmetries in PDEs, you can check the list of publications in MSC class 35B06. For the mathematical physics journals, I suggest trying to find the proper MSC class in the MSC catalog, there you can see which journals would be suitable.