V. I. Karpman | Searcharxiv

arXiv2002

Envelope Solitons of Nonlinear Schrodinger Equation with an Anti-cubic Nonlinearity

On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrodinger equations [1]-[3], the existence of an envelope solitonlike solutions of a nonlinear Schrodinger equation containing an anti-cubic nonlinearity (|Psi|^{-4} Psi) plus a "regular" nonlinear part is investigated. In particular, in case the regular nonlinear part consists of a sum of a cubic and a quintic nonlinearities (i.e. q_1 |Psi|^2 Psi + q_2 |Psi|^4 Psi), an upper-shifted bright envelope solitonlike solution is explicitly found.

nlin.PS↗

arXiv2001

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

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.

nlin.SI↗