We carry on a comprehensive study static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible application of this kind fluids requires extreme conditions where quantum effects expected play an important role. Also, it is found the distribution cannot fill ...

We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The transformation is then identified with sequence four mutations. As an application the new formalism we show how to construct integrable system spectral curve arbitrary symmetric Newton polygon. Finally, embed this into double Bruhat cel...

The axially symmetric non-local solution in the Heisenberg equation is found. It is regular in the whole space and has the finite energy on the unit of length according to this we may consider the solution as a string. Taking the non-local spherically symmetric solution, which was found by Finkelstein et. al., and our solution in account we suggest to consider the Heisenberg equation as a quant...

In this paper, we consider multi-component generalizations of the Hirota–Satsuma coupled Korteweg–de Vries (KdV) equation. By introducing a Lax pair, we present a matrix generalization of the Hirota–Satsuma coupled KdV equation, which is shown to be reduced to a vector Hirota–Satsuma coupled KdV equation. By using Hirota's bilinear method, we find a few soliton solutions to the vector Hirota–Sa...