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

Considering the magneto-hydrodynamic equations in a non-relativistic multi uid framework, we study the behavior of small amplitude perturbations in cold quark matter. Magneto-hydrodynamic 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 modied form of the derivative nonlinear Schrodinger equation instead of the KdV equation. Considering the magnetic eld 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 eld component along the direction of magnetic eld 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 eld (at the scale of compact stars).