[fdej]

You should be able to understand everything in that sentence if you have taken a typical undergraduate curriculum in physics including quantum mechanics and electromagnetism. Though it depends on what you mean by "understand". It should be clear what "quantised magnetic flux" is roughly about, but I have no idea what constitutes the "modern knowledge of quantised magnetic flux" in this context.

[sp332]

That doesn't help with the first part, about a phase vortex in compressible inviscous liquids.