اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUnstable gap solitons in inhomogeneous Schrodinger equations
455
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A periodically inhomogeneous Schrodinger equation is considered. The inhomogeneity is reflected through a non-uniform coefficient of the linear and non-linear term in the equation. Due to the periodic inhomogeneity of the linear term, the system may admit spectral bands. When the oscillation frequency of a localized solution resides in one of the finite band gaps, the solution is a gap soliton, characterized by the presence of infinitely many zeros in the spatial profile of the soliton. Recently, how to construct such gap solitons through a composite phase portrait is shown. By exploiting the phase-space method and combining it with the application of a topological argument, it is shown that the instability of a gap soliton can be described by the phase portrait of the solution. Surface gap solitons at the interface between a periodic inhomogeneous and a homogeneous medium are also discussed. Numerical calculations are presented accompanying the analytical results.
قيم البحث
اقرأ أيضاً
We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local refractive index, and periodic variation of the local reflec
tivity. We demonstrate that, while the previously studied reflectivity modulation strongly destabilizes all solitons, the periodic chirp modulation, which is a novel feature, stabilizes a new family of double-peak fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and keeps solitons stable in the central bandgap (No. 0). The two soliton families demonstrate bistability, coexisting at equal values of energy. In addition, stable 4-peak bound states are formed by pairs of fundamental GSs in bandgap -1. Self-trapping and mobility of the solitons are studied too.
We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schrodinger equations, coupled by repulsive XPM (cross-phase-modulation) terms, in the absence of the SPM (self-phase-modulation) nonlinearity. T
he equations include a periodic potential acting on both components, thus giving rise to GSs of the symbiotic type, which exist solely due to the repulsive interaction between the two components. The model may be implemented for holographic solitons in optics, and in binary bosonic or fermionic gases trapped in the optical lattice. Fundamental symbiotic GSs are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. Symmetric solitons are destabilized, including their entire family in the second bandgap, by symmetry-breaking perturbations above a critical value of the total power. Asymmetric solitons of intra-gap and inter-gap types are studied too, with the propagation constants of the two components falling into the same or different bandgaps, respectively. The increase of the asymmetry between the components leads to shrinkage of the stability areas of the GSs. Inter-gap GSs are stable only in a strongly asymmetric form, in which the first-bandgap component is a dominating one. Intra-gap solitons are unstable in the second bandgap. Unstable two-component GSs are transformed into persistent breathers. In addition to systematic numerical considerations, analytical results are obtained by means of an extended (tailed) Thomas-Fermi approximation (TFA).
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic func
tions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum and parity for alpha particle clustering nuclei.
We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line
approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrodinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.
Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schr{o}dinger / Gross-Pitaevski
i Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, and G. Schneider, J. Nonlin. Sci. {bf 19}, 95--131 (2009)] the CME derivation has to be carried out in Bloch rather than physical coordinates. Using the Lyapunov-Schmidt reduction we then give a rigorous justification of the CMEs as an asymptotic model for reversible non-degenerate gap solitons and even potentials and provide $H^s$ estimates for this approximation. The results are confirmed by numerical examples including some new families of CMEs and gap solitons absent for separable potentials.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
