# Solitary Waves Under The Competition Of Linear And Nonlinear Periodic Potentials

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### Hidden vorticity in binary Bose-Einstein condensates

nonlinear terms [8], an example relevant to BECs being the stabilization of solitary vortices by the long-range dipole-dipole interactions [9]). In the 2D geometry, matter-wave solitons of the vortex type can be stabilized by an external potential periodic in x and y (optical lattice) [3,10], although

### Whitham averaged equations and modulational stability of

nonlinear stability theory for these waves. For the physically relevant system (1.2), it turns out that we are able to perform a complete spectral, linear, and nonlinear stability analysis of the associated periodic traveling wave solutions. Indeed, although the abstract nonlinear stability theory of [JZ2], developed

### Nonlinear optics of periodic and quasiperiodic structures

nonlinear periodic media the coupled mode theory19 as well as the envelope function approach20 have been quite popular. The major outcome of the studies on Kerr nonlinear periodic media has been the prediction of solitary wave profiles with the frequency in the stop gap of the struc ture. The static (immobile) profiles, termed as 'gap

### Power dependent soliton location and stability in complex

the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics.

### Whitham averaged equations and modulational stability of

Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law J. É. D. P. (2010), Exposé n o III, 24 p.

### Propagation of periodic patterns in a discrete system with

waves, motion of domain walls, phase boundaries and dislocations, solitary waves, discrete breathers and many other phenomena where spatial discreteness plays an important role [5, 9, 12, 22, 27, 30]. The interplay between ﬀt interactions in a spatially discrete system often leads to formation of periodic patterns.

### Attenuation of long interfacial waves over a randomly rough

& Solna (2003), for linear waves. For weak ﬂuctuations and weakly nonlinear long waves Rosales & Papanicolaou (1983) gave an asymptotic theory on the change of phase speed by randomness. Gas extraction from the North Sea is a current project in the new gas ﬁeld of Ormen Lange on the Norwegian continental shelf.† A 1200km pipe line of 0.75m

### Списък на цитиранията на публикациите

12) J.-R.He, H.-M. Li, Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials, Physical Review E 83, 6, art. no. 066607 (2011). 13) J. Lægsgaard, Trapping of slow solitons by longitudinal inhomogeneity in

### One-dimensional gap solitons in quintic and cubic quintic

competition between self-focusing cubic and self- periodic potential (linear lattice) into this model and the propagation of linear and nonlinear waves in dif-

### University of Bath

related results. Here we consider a nonlinear context and prove under suitable conditions the persistence of periodic waves for all subsonic speeds and also, more unexpectedly, for a small range of supersonic speeds. 2. The mathematical setting We are looking for periodic solutions of the equation (1). We write U 1 2 2 1(r) = c 0r + V (r) (2) 2 and

### Algebraic bright and vortex solitons in defocusing media

depends on the inte nsity of the nonlinear excitation [2]. Many effects were predicted in no nlinear [3 - 7] and mixed linear-nonlinear [8-14] lattices, in both one - (1D) and two -dimensional (2D) [15- 17] settings. However, in contrast to linear lattices, localized and periodic l andscapes of defocusing no n-

### P h y si c a l C hemi ournal of Physical Chemistry Toko et al

can describe the propagation of solitary waves by invoking a discrete Jacobian elliptic function method. These solutions include the Jacobian periodic solution as well as bubble solitons. Through the Fourier series approach, we have found that the DNA dynamics is governed by a modified discrete nonlinear Schrodinger (MDNLS) equation. A detailed

### Light bullets in Bessel optical lattices with spatially

even BECs in periodic nonlinear lattices [20-24]. Engineering the linear refractive index together with the nonlinearity may be also possible in optical structures, e.g., in photonic crystals with the holes infiltrated with a highly nonlinear material, such as suitable index-matching liquids [25-28].

### Mobility of solitons in one-dimensional lattices with the

is sensitive to the intensity of traveling waves, nonlinear corrections must be included in the description of the wave propagation, which often leads to adequate models based on nonlinear partial differential equations (PDEs). Solitary-wave solutions, or solitons, are robust localized modes generated by this type of nonlinear evolution equations.

### Whitham averaged equations and modulational stability of

nonlinear stability under these conditions. We then turn to an analytical and numerical investigation of the veriﬁcation of these spectral stability assumptions. While spec-tral instability is shown analytically to hold in both the Hopf and homoclinic limits, our numerical studies indicates spectrally stable periodic solutions of intermediate pe-

### Solitary waves under the competition of linear and nonlinear

Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials Z. Rapti1, P.G. Kevrekidis2, V.V. Konotop3, C.K.R.T. Jones4 1 Department of Mathematics University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2975 2 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003

### Light bullets in Bessel optical lattices with

even BECs where periodic nonlinear lattices are created [20-24]. Engineering both, the linear re-fractive index and the nonlinearity may be also possible in optical structures, e.g., in photonic crystals with the holes infiltrated with a highly nonlinear material, for example index-matching nonlinear liquids [25-28].

### Solitary waves under the competition of linear and nonlinear

Aug 02, 2019 Solitary waves under the competition of linear and nonlinear periodic potentials Z Rapti1, P G Kevrekidis2, V V Konotop3,4 and C K R T Jones5 1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2975, USA 2 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA

### A discrete variational approach for investigation of

ample of a diﬀerential discrete nonintegrable nonlinear equation, having solitary wave solutions. Most importantly, the existence of solitary waves in the N-AL equation can be shown analytically [46]. The solitary wave solutions of these equations have continuous translational symmetry, which can be seen from the analytical expression of the one-

### Charged particle nonlinear resonance with localized

onant interaction of such waves with charged particles is essentially nondi usive and includes nonlinear e ects like phase trapping and phase bunching (scattering) [e.g., 19, 20, and references therein]. Therefore, there is an open question: how to describe the long-term evolution of the charged particle velocity distribution in the system

### Nonlinear Dirac equation solitary waves under a spinor force

Nov 29, 2019 Nonlinear Dirac equation solitary waves under a spinor force with different components To cite this article: Franz G Mertens et al 2017 J. Phys. A: Math. Theor. 50 145201 View the article online for updates and enhancements. Related content Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

### Analytic solutions for nonlinear waves in coupled reacting

Fig. 1. The potentials ofthe mechanical analog ofEq. (4). The cases shown areV and V˜, corresponding to faster than v and slower than v traveling waves respectively. waves, will be dierent from v, the speed ofthe linear waves dictated by the medium. The ordinary dierential equation describing the shape ofthe wave is (c2 −v2)U =kf(U)=− @V