Multi fluidity and Solitary wave stability in cold quark matter: core of dense astrophysical objects

Considering the magneto-hydrodynamic equations in a nonrelativistic multi uid framework, we study the behavior of small amplitude perturbations in cold quark matter. Magnetohydrodynamic equations, along with a suitable equation of state for the cold quark matter, are expanded using the reductive perturbation method. It is shown that in small amplitude approximation, such a medium should be considered as a multi uid system. The result is a nonlinear wave equation which complies with a modified form of the derivative nonlinear Schrodinger equation instead of the KdV equation. Considering the magnetic field which is supported by the Maxwell’s equations, we show that the complete set of equations, create stable solitary waves. An interesting result is the existence of an electric field component along the direction of magnetic field which causes a small charge separability in the medium. Properties of this solitonic solution are studied by considering different values for the environmental characters such as background mass density and strength of the magnetic field (at the scale of compact stars).