相关论文: Generic transverse stability of kink structures in…
We unravel stationary states in the form of dark soliton stripes, bubbles, and kinks embedded in a two-dimensional droplet-bearing setting emulated by an extended Gross-Pitaevskii approach. The existence of these configurations is…
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…
A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1+1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky (KD) equation. We show that these waves are transversely unstable with…
The occurrence of energetic and dynamical instabilities in a Bose-Einstein condensate moving in a one-dimensional (1D) optical lattice is analyzed by means of the Gross-Pitaevskii theory. Results of full 3D calculations are compared with…
We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The…
We show analytically, numerically, and experimentally that a transversely stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made…
We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and…
We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the…
The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates dark solitons are unstable against transverse excitations in two and three dimensions. On the…
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and…
We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of…
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…
Several experimental groups are currently working towards realizing quasi-one-dimensional (1D) atom waveguides and loading them with ultracold atoms. The dynamics becomes truly 1D in a regime (Tonks gas) of low temperatures and densities…
We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross-Pitaevskii model including the Lee-Huang-Yang…
Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
We study transverse stability and instability of one-dimensional small-amplitude periodic traveling waves of a generalized Kadomtsev-Petviashvili equation with respect to two-dimensional perturbations, which are either periodic or…