Nonlinear Dirac equation solitary waves in the presence of external driving forces (original) (raw)

This work explores the nonlinear Dirac equation (NLD) in 1+1 dimensions under the influence of external forces and damping. An approximate variational approach is employed, revealing that solitary waves experience intrinsic oscillations in amplitude, width, and phase while maintaining a mean trajectory. The variational results demonstrate good agreement with numerical simulations, particularly when accounting for linear excitations. Furthermore, the canonical momentum conservation principle is examined across various conditions.