Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation.

The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrödinger equation is studied. 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)-->0. The most essential, at small alpha(3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton).

Radiation of solitons described by a high-order cubic nonlinear Schrodinger equation.

The resonant radiation of solitons due to higher order dispersion, described by an extended nonlinear Schrodinger (NLS) equation with nonlinear (cubic) dispersive terms and linear terms with third and fourth derivatives, is studied. The basic equation includes, as a particular case, a higher order derivative NLS equation. General properties of the master equation, such as conservation laws, Hamiltonian structures (in important particular cases), and Galilei transformation are studied.