Internal modes of envelope solitons
نویسندگان
چکیده
We extend the concept of internal mode to envelope solitons and show that this mode is responsible for long-lived, weakly damped periodic oscillations of the soliton amplitude observed in numerical simulations. We present analytical and numerical results for solitons of the generalized nonlinear S chr6dinger equation and analyze the example of the cubic-quintic nonlinearity in more detail. We obtain also analytical criteria for the existence and bifurcations of the soliton internal mode and calculate the rate of the radiation-induced damping of the soliton oscillations induced by excitation of the internal mode. Copyright © 1998 Elsevier Science B.V. PACS: 42.65.Tg; 63.20.Pw; 52.35.Mw; 03.40.Kf
منابع مشابه
Internal Oscillations and Radiation Damping of Vector Solitons
Internal modes of vector solitons and their radiation-induced damping are studied analytically and numerically in the framework of coupled nonlinear Schrödinger equations. Bifurcations of internal modes from the integrable systems are analyzed, and the region of their existence in the parameter space of vector solitons is determined. In addition, radiation-induced decay of internal oscillations...
متن کاملBubblelike structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons.
Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubbleli...
متن کاملBifurcations and stability of gap solitons in periodic potentials.
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap solitons from the band edges of the Floquet-B...
متن کاملHow to excite the internal modes of sine-Gordon solitons
We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic timedependent forces can sustain oscillations of the soliton width. We sh...
متن کاملRole of internal and continuum modes in modulational instability of quadratic solitons.
The role of internal and continuum modes in the modulational instability of spatial quadratic solitons is examined by asymptotic and numerical analyses. It is shown that these modes generate novel spatially symmetric and asymmetric modulation instability branches, which underline soliton dynamics throughout a wide region of the wave-vector mismatch.
متن کامل