Thank you for the great "morning coffee literature"
Spoiler Alert for those who like to be stunned while reading the papers
The first paper was friendly for non-physics people. Different objects are producing solitons of different compactness. Nice to know, although I haven't understood why are they asymmetrical.
The second one had a mindblowing sentence:
the gravitational wave is absent. However, these electromagnetic waves produce some running longitudinal deformations of spacetime (of metric components on (t, x)-plane).
I guess that this is the answer to my question
There may be other papers. Will continue looking, but not now (waiting for boarding a flight, which is not that practical ;) ).