We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized wav...We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.展开更多
Two fundamental facts of the modern wave turbulence theory are 1)existence of power energy spectra in k-space,and 2)existence of“gaps”in this spectra corresponding to the resonance clustering.Accordingly,three wave ...Two fundamental facts of the modern wave turbulence theory are 1)existence of power energy spectra in k-space,and 2)existence of“gaps”in this spectra corresponding to the resonance clustering.Accordingly,three wave turbulent regimes are singled out:kinetic,described by wave kinetic equations and power energy spectra;discrete,characterized by resonance clustering;and mesoscopic,where both types of wave field time evolution coexist.In this review paper we present the results on integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes.Using a novel method based on the notion of dynamical invariant we show that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others-only for particular initial conditions.We also identify chaotic behaviour in some cases.Physical implications of the results obtained are discussed.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11475135,11547302,11434013 and 11425522
文摘We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.
基金funded by European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce(Contract No.026133)E.Kartashova acknowledges the support of the Austrian Science Foundation(FWF)under projects P20164 and P22943.
文摘Two fundamental facts of the modern wave turbulence theory are 1)existence of power energy spectra in k-space,and 2)existence of“gaps”in this spectra corresponding to the resonance clustering.Accordingly,three wave turbulent regimes are singled out:kinetic,described by wave kinetic equations and power energy spectra;discrete,characterized by resonance clustering;and mesoscopic,where both types of wave field time evolution coexist.In this review paper we present the results on integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes.Using a novel method based on the notion of dynamical invariant we show that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others-only for particular initial conditions.We also identify chaotic behaviour in some cases.Physical implications of the results obtained are discussed.
