Bäcklund Transformations and Exact Solutions for Alfvén Solitons in a Relativistic Electron–Positron Plasma

Nonlinear Alfvén waves, propagating along a homogeneous magnetic field, are studied using relativistic isotropic hydrodynamics. Alfvén solitons of the moving-wave and wave packet types are considered for modified Korteweg–de Vries (mKdV) equation and the nonlinear Schrödinger (NLS) equation, respectively. The method of characteristics is used and the Bäcklund transformations (BTs) are employed to generate new solutions from the old ones. Thus, families of new solutions for the mKdV and the NLS equations are obtained. The question arises which solitons exist in the pulsar atmosphere.