相关论文: Modulation instability and non-degenerate Akhmedie…
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We consider the \emph{focusing} nonlinear Schr\"odinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study…
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H^2 topology. Our proof introduces a new Lyapunov functional, at the H^2 level, which allows to describe the dynamics of small…
In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into an…
Optical rogue waves and its variants have been studied quite extensively in the context of optical fiber in recent years. It has been realized that dispersion management in optical fiber is experimentally much more feasible compared to its…
We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
Breathers and rogue waves of special coupled nonlinear Schr\"odinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence.…
We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves,…
In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in [17], in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev…
A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small…
We numerically investigate azimuthal modulation instability in an optical fiber supporting orbital angular momentum modes only, i.e. a vortex fiber, by means of the scalar multimode unidirectional pulse propagation equation. We demonstrate…
We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schr\"{o}dinger Equation. We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by…
We study beating solitons and their interaction for the three-component nonlinear Schr\"odinger equations (NLSEs) in both focusing and defocusing cases. We identify a previously unknown family of beating solitons with nonzero relative…
We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor,…
It is well known that Akhmediev breathers of the nonlinear cubic Schrodinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each…
Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in…
The nonlinear Schr\"{o}dinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate. Apart from the usual bright and dark-soliton…
A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is…
The Akhmediev breather (AB) solution of the nonlinear Schr$\"{o}$dinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution.…