Well, if I had to guess, I would say that they are going to have to redesign the front gear on the J-15.
Just from the looks of it, as compared to the F-18 you show, it is a very tall gear without the major, beefy support struts coming off of it. You can see that support coming back from the middle of the F-18's nose gear. What there is on the J-15 is much smaller and much higher up.
I was honored to work on the later variants of the A-7 Corsair II. In that case the aircraft sat somewhat lower to the deck, and the front gear itself had the wheels on the back side of an angled apparatus, where the point of that apparatus was forward, with a heavy strut down to the wheels, and another strut angling up into the aircraft where it was anchored. It was an ingenious design. Take a look at its gear and you will see that it is not a straight down to the wheels with a heavy brace mid way up. The gear holding the wheels was actually part of the brace.
As to the J-15, a cat is going to put a huge moment arm on that gear, and I think it is going to have to be redesigned to provide the necessary support.
But again, that's just my impression, not knowing precisely what materials are being used and how they are being anchored, one cannot say for certain, but looking at it, if I had to guess, I would say that the front gear is likely to have to be redesigned for catapult operations.