The Klein–Fock–Gordon equation (KFGE), defined as the of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful a model several types matter, with deviation in basic stuffs particles crystals. In this work, Sardar subequation method (SSM) used finding solution KFGE. advantage SSM that it provides many different kinds solitons, such dark, bright, ...

We derive the non-relativistic limit of a massive vector field. show that Cartesian spatial components behave as three identical, non-interacting scalar fields. find classes spherical, cylindrical, and planar self-gravitating solitons in Newtonian limit. The gravitational properties lowest-energy solitons$\mathrm{-}$the potential density field$\mathrm{-}$depend only on net mass soliton particle...

In this paper, at first we have formulated the lowest order constrained variational method for the relativistic case of an interacting fermion system at finite temperature. Then we have used this formalism to calculate some thermodynamic properties of liquid in the relativistic regime. The results show that the difference between total energies of relativistic and non-relativistic cases of liqu...

We derive an exact equation of motion for a non-relativistic vortex in twoand three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom. Talk presented by O.T. a...

Three dimensional relativistic electromagnetic sub-cycle solitons were observed in Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in-phase with the electron density with frequency below the Langmuir freque...