Nonlinear vector field having an exact particle-like solution with finite energy and phase wave

A model relativistically invariant Lagrangian corresponding to a nonlinear wave equation (with three arbitrary constants $m_1$, $m_2$, and $m_3$) for a complex four-vector field and exact particle-like solutions to this equation are given. The energy, momentum, “charge”, and spin of the corresponding “particles” are calculated as functions of $m_1$, $m_2$, $m_3$. The values of $m_1$, $m_2$, $m_3$ at which the particle parameters agree with the corresponding parameters of the $\rho$ mesons are given. For these values of $m_1$, $m_2$, and $m_3$, the nonlinearity of the field is effectively manifested only within the limits of a particle.