Solitary and periodic waves in two-fluid magnetohydrodynamics

• A system of equations of two-fluid magnetohydrodynamics is studied.
• The Painlevé analysis of this equation is carried out.
• The general solution of the equation is constructed in terms of the Weierstrass elliptic function.
• Solitary and periodic wave solutions for the components of magnetic field are found.

A system of equations of two-fluid magnetohydrodynamics is studied. An ordinary differential equation describing traveling waves in an ideal cold quasi-neutral plasma is obtained in the case of quasi-stationary electromagnetic field. The Painlevé analysis of this equation is carried out and the general solution of the equation is constructed in terms of the Weierstrass elliptic function. Solitary and periodic wave solutions for the components of magnetic field are found and analyzed.