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Speed-of-light pulses in a massless nonlinear dirac equation
(American Physical Society, 2019)
In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two ...
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From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates
(2014)
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear ...
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Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management
(Elsevier, 2018)
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity ...
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Revisiting multi-breathers in the discrete Klein–Gordon equation: a spatial dynamics approach
(IOP Publishing, 2022-11)
We consider the existence and spectral stability of multi-breather structures in the discrete Klein–Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a ...
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Using the finite domain remnant of the continuous spectrum to examine integrability: Effect of boundary conditions
(2003)
The aim of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE), by examining it in a finite but large domain. For monoparametric ...
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Stability of Solitary Waves and Vortices in a 2D Nonlinear Dirac Model
(American Physical Society (APS), 2016)
We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral ...
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Solitary waves in the Ablowitz--Ladik equation with power-law nonlinearity
(IOP Publishing, 2019)
We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr¨odinger equation with the same type of the nonlinearity. The model opens a ...
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Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points
(Elsevier, 2020-06)
We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and ...
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Nucleation of breathers via stochastic resonance in nonlinear lattices
(2009)
By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the spontaneous formation and destruction of discrete breathers with a selected frequency due to thermal ...
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Experimental and numerical observation of dark and bright breathers in the band gap of a diatomic electrical lattice
(American Physical Society, 2019)
We observe dark and bright intrinsic localized modes (ILMs), also known as discrete breathers, experimentally and numerically in a diatomic-like electrical lattice. The experimental generation of dark ILMs by driving ...