相关论文: Discrete instability in nonlinear lattices

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling…

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal…

In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…

A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. For [$\chi ^{(3)}$] nonlinearity, the model finds two different…

We study pattern-forming nonlinear dynamics starting from a continuous wave state of quasi-one-dimensional two-component Bose-Einstein condensates with synthetic spin-orbit coupling induced by Raman lasers. Modulation instability can occur…

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the…

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find…

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…

In this paper we address the issue of stability for the near-inertial Pollard waves, as a model for the halocline in the region of the Arctic Ocean centered around the North Pole, derived in Puntini (2026). Adopting the short-wavelength…

Local linear instability refers to the linearized discrete operator exhibiting perturbation growth exceeding that of the corresponding continuous linearized problem. In the context of nonlinear entropy-stable discretizations, we argue that…

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…

The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient…

The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the…

The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…

Thanks to their immense purity and controllability, dipolar Bose-Einstein condensates are an exemplar for studying fundamental non-local nonlinear physics. Here we show that a family of fundamental nonlinear waves - the dark solitons - are…

Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…

We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum…

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…