Related papers: Continuous-wave solutions and modulational instabi…
Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integro-differential equation, a nonlocal system and a…
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non-variational Slonczewski term for spin-torque effects.…
The cubic-vortical Whitham equation is a model for wave motion on a vertically sheared current of constant vorticity in a shallow inviscid fluid. It generalizes the classical Whitham equation by allowing constant vorticity and by adding a…
We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…
We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles, and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the…
We consider front solutions of the Swift-Hohenberg equation $\partial_t u= -(1+\partial_x^2)^2 u +\epsilon ^2 u -u^3$. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization…
We study the stability of collective amplitude excitations in non-equilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors.…
Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust particles as…
Linear analysis of the stability of diffuse clouds in the cold neutral medium with uniform magnetic field is performed. We consider that gas in equilibrium state is heated by cosmic rays, X-rays and electronic photoeffect on the surface of…
On dielectric periodic structures with a reflection symmetry in a periodic direction, there can be antisymmetric standing waves (ASWs) that are symmetry-protected bound states in the continuum (BICs). The BICs have found many applications,…
We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates the dispersion relation of surface water waves and the nonlinearity of the shallow water equations,are spectrally unstable…
We study the nature of the two-dimensional quantum critical point separating two phases with and without long-range spin-density-wave order, which has been recently observed in cuprate superconductors. We consider the Landau-Ginzburg-Wilson…
Amplitude modulation of quantum ion-acoustic waves (QIAWs) in a quantum electron-pair-ion plasma is studied. It is shown that the quantum coupling parameter $H$ (being the ratio of the plasmonic energy density to the Fermi energy) is…
We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multi-component Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a…
Unconventional charge and spin density-wave states are commonly observed in bilayer nickelates, drawing considerable attention due to their proximity to high-$T_c$ superconductivity in various phase diagrams. However, the nature and…
We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions…
We present a self-consistent mean field model of the extraction of atoms from a Bose-Einstein condensate to form a CW atom laser. The model is based upon the Hartree-Fock Bogoliubov equations within the Popov approximation, modified by the…
The present paper is concerned with large-time behavior of solutions to an outflow problem for an ideal polytropic model of compressible viscous gases in one-dimensional half space, and with a convergence rate of solutions toward a…
We study the linear dynamics of spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. Such $T$-periodic solutions…
In this paper, we consider the nonlinear fractional Schr\"odinger equations with Hartree type nonlinearity. We obtain the existence of standing waves by studying the related constrained minimization problems by applying the…