  In a model of nonlinear system of three scalar fields the problem on dynamics
of a massive particle moving in effective potential provided by two
relativistic fields is solving. The potentials for these fields are chosen in
the form of anti-Higgs and Higgs potentials. It is shown that the effective
potential has the shape of two-hump barrier localized in spacetime. It tends to
constant attractive potential at spacetime infinity. The magnitude of this
constant constituent is determined by the Higgs condensate. It is shown that
nonlinear equation of motion of a particle has the solutions which describe the
capture of a particle by the barrier and the scattering on the barrier.
