Polyethylene glue is an 'urban myth'. Modern polyethlene materials are purposely so chemical resistant that no glue has yet been made that will bond them ! Polyethylene pipes are bonded by 'hot air' welding, not by any glues. They can be held together by contact adhesives, but the joint is very weak and will not hold even 30psi of water or air pressure.
Super glue will not stick to polyethylene or CPVC.
Double sided foam tape is a permanent bonding solution as a cold glue alternative for a polyethylene tarp adhering to another polyethylene tarp. There is no solvent that has been specifically made as a cold glue for polyethylene but are solutions as alternatives.
High density polyethylene foam. Use heat. Non foam plastic use super glue.
No, there are big differences in the chemical composition.
Hot welding with a polyethylene stick is the only way. No glue has yet been made that will effectively adhere to polyethylene.
I recommend a product called Goop.
With a polycarbonate glue. Try Weld On # 3 or #16.
Epoxy will glue almost all plastics with the exception of the 'slippery' ones like polypropylelen, polyethylene, PEX, CPVC, and similar.
Polyethylene is one of those very slippery new plastics that nobody has developed a suitable glue for. -In plumbing use, it's 'hot air welded' and even in simple pipe application thre is no transfer cement or glue that will melt it. If I had your problem, I would try to find a suitable 'mechanical' method -possibly screws or rivets.
That's HIGH DENSITY, or HDPE in the plumbing business. Pro-Poly is one of the very few choices for this. The fact is that the group of olefins (polyethylene based plastics), which include LDPE, HDPE, and UHMW, are so chemical resistant that modern science has not invented a solvent glue to bond these plastics.
It is safe when dried,- but it may not work on many food containers, especially those made with polyethylene.
Polyethylene Which is stronger Polyethylene or dyneema?