Variational approach to the interaction dynamics of nonlinear compressional Alfvén waves and moving charged obstacle

The nonlinear interactions of compressional Alfvén wave and a steadily moving charged obstacle are examined in Hall magnetohydrodynamics (MHD). The interaction dynamics is shown to be described by a forced derivative nonlinear Schrödinger equation (fDNLSE). The steadily moving charged obstacle induced weak perturbation is responsible for the forcing term. The variational structure is used to investigate the exact solitary wave solutions of the fDNLSE for a special analytic form of the forcing term by constructing a proper Hamiltonian of the system. The conditions for the stability of these solitary waves are delineated through variational method. The numerical solutions using the split-step Fourier method confirm the analytical results representing the pinned solitons. The relevance and potential applications of the results in astrophysics are also discussed.