Abstract: In this paper, we consider some integrable Heisenberg
Ferromagnet Equations with self-consistent potentials. We study
their Lax representations. In particular we derive their equivalent
counterparts in the form of nonlinear Schr¨odinger type equations.
We present the integrable reductions of the Heisenberg Ferromagnet
Equations with self-consistent potentials. These integrable Heisenberg
Ferromagnet Equations with self-consistent potentials describe
nonlinear waves in ferromagnets with some additional physical fields.
Abstract: In this paper we consider the equation of motion for
the F (R, T) gravity on their property of conformal invariance. It
is shown that in the general case, such a theory is not conformal
invariant. Studied special cases for the functions v and u in which
can appear properties of the theory. Also we consider cosmological
aspects F (R, T) theory of gravity, having considered particular case
F (R, T) = μR+νT^2. Showed that in this case there is a nonlinear
dependence of the parameter equation of state from time to time,
which affects its evolution.
Abstract: In this letter, we explore exact solutions for the
Horava-Lifshitz gravity. We use of an extension of this theory with
first order dynamical lapse function. The equations of motion have
been derived in a fully consistent scenario. We assume that there
are some spherically symmetric families of exact solutions of this
extended theory of gravity. We obtain exact solutions and investigate
the singularity structures of these solutions. Specially, an exact
solution with the regular horizon is found.