We obtain solutions of the time-dependent Einstein Field Equations which satisfy Karmarkar condition via method Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal flatness, Weyl-free collapse and shear-free collapse. In particular, a solution was found satisfies heat-flux boundary Santos, radiating stellar model then obtained investiga...

In this paper the classical Lie group formalism is applied to deduce new classes of solutions of a less studied nonlinear partial differential equation (nPDE) of the third order. The nPDE under consideration is closely related to motions of plane curves. Up to now no carefully performed symmetry analysis is available. Therefore we determine the classical Lie point symmetries including algebraic...

The nonlocal symmetry of the new (3+1)-dimensional Boussinesq equation is obtained with truncated Painlevé method. can be localized to Lie point for prolonged system by introducing auxiliary dependent variables. finite transformation related integrable studied. Meanwhile, proved consistent tanh expansion method and many interaction solutions among solitons other types nonlinear excitations such...