  A nonlinear dispersion of a general stationary wave in collisionless plasma
is obtained in a non-differential form from a single-particle
oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized
plasma, considered as a paradigmatic example, the linear dielectric function is
generalized, and the trapped particle contribution to the wave frequency shift
$\Delta\omega$ is found analytically as a function of the wave amplitude $a$.
Smooth distributions yield $\Delta\omega\sim a^{1/2}$, as usual. However,
beam-like distributions of trapped electrons result in different power laws, or
even a logarithmic nonlinearity, which are derived as asymptotic limits of the
same dispersion relation.
