Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-02-08
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.1103/PhysRevE.64.026614
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.
Karpman V. I.
Rasmussen Jorgen
Shagalov A. G.
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