相关论文: Surface gap solitons at a nonlinearity interface
We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media.…
In this paper, we consider capillary-gravity waves propagating on the interface separating two fluids of finite depth and constant density. The flow in each layer is assumed to be incompressible and of constant vorticity. We prove the…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
We study fundamental optical gap solitons in the model of a fiber Bragg grating (BG), which is subjected to a periodic modulation of the local reflectivity, giving rise to a supergrating. In addition, the local refractive index is also…
Parity-time(PT) symmetric lattices have been widely studied in controlling the flow of waves, and recently moir\'e superlattices, connecting the periodic and non-periodic potentials, are introduced for exploring unconventional physical…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
Existence and stability of PT-symmetric gap solitons in a periodic structure with defocusing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable…
A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the…
We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant…
Using the variational approximation(VA) and direct simulations, we find stable 2D and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction ($z$) and periodic in the others…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
We develop a detailed rigorous analysis of edge bifurcations of standing waves in the nonlinear Schr\"odinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the…
We analyze the existence, stability, and mobility of gap solitons in a periodic photonic structure with nonlocal nonlinearity. Within the Bragg region of band gaps, gap solitons exhibit better stability and higher mobility due to the…
We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The objective of the work is to investigate solitons and their stability in this system. New…
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free…
We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…
Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and…
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…
Much like their counterparts in homogenous elastic solids, waves in periodic media can be broadly classified into Floquet-Bloch body waves, and evanescent surface waves. Our goal is to elucidate the latter boundary layers, termed surface…