Miscellaneous Rotating Solitary Waves to a Coupled Dispersionless System

We investigate the soliton structure of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following Hirota's method, we unwrap three typical localized waves with nonzero angular momentum depending strongly upon their angular velocities. Illustrating the soliton behavior of these waves, we focus our interests on breather-like waves and depict the elastic scattering amongst such waves.