  The dynamics of soliton and quasisoliton solutions of cubic third order
nonlinear Schr\"{o}dinger equation is studied. The regular solitons exist due
to a balance between the nonlinear terms and (linear) third order dispersion;
they are not important at small $\alpha_3$ ($\alpha_3$ is the coefficient in
the third derivative term) and vanish at $\alpha_3 \to 0$. The most essential,
at small $\alpha_3$, is a quasisoliton emitting resonant radiation (resonantly
radiating soliton). Its relationship with the other (steady) quasisoliton,
called embedded soliton, is studied analytically and in numerical experiments.
It is demonstrated that the resonantly radiating solitons emerge in the course
of nonlinear evolution, which shows their physical significance.
