Dynamics of Solitons and Quasisolitons of Cubic Third-Order Nonlinear Schrödinger Equation

Abstract

The dynamics of soliton and quasisoliton solutions of cubic third order nonlinear Schrödinger 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 $α_3$ ($α_3$ is the coefficient in the third derivative term) and vanish at $α_3 \to 0$. The most essential, at small $α_3$, 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.