Abstract:
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.
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