The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the inter–grain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the ...

Coherent nonlinear structures in the form of vortical motions are frequently observed in laboratory devices and in auroral plasmas. Our objective here is to suggest that any realistic description of plasma vortices must involve three-dimensional nonlinear wave models, which account for the nonlinear coupling between finite amplitude electrostatic and/or electromagnetic disturbances. Specificall...

We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the w...

Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...

In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...

The nonlinear propagation of low-frequency circularly polarized waves in a magnetized dusty plasma is analyzed. It is found that wave steepening and shock formation can take place due to the presence of nonlinear quantum vacuum effects, thus giving rise to ultra-intense electromagnetic shocks. Moreover, it is shown that solitary wave structures are admitted even under moderate astrophysical con...

We propose a simple general method for analytic determination of the boundaries of the expanding nonlinear oscillation zone occurring in the decay of a step problem for non-integrable dispersive wave equations. A remarkable feature of the method is that it essentially uses only the dispersionless limit and the linear dispersion relation of the original nonlinear dispersive wave system. A concre...

Theoretical and numerical studies are presented of the nonlinear amplitude modulation of dustacoustic (DA) waves propagating in an unmagnetized three component, weakly-coupled, fully ionized plasma consisting of electrons, positive ions and charged dust particles, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrödinge...

In this article, we use the general theory derived in Paper I [M. Tacu and D. Bénisti, Phys. Plasmas 29, 052108 (2022)] order to address several long-standing issues regarding nonlinear electron plasma waves (EPWs). First, discuss relevance practical usefulness of stationary solutions Vlasov–Poisson system, so-called Bernstein–Greene–Kruskal modes, model slowly varying waves. Second, derive an ...

Repeated, self-excited dust acoustic shock waves (DASWs) have been observed in a dc glow discharge dusty plasma using high-speed video imaging. Two major observations are reported: (1) The self-steepening of a nonlinear dust acoustic wave (DAW) into a saw-tooth wave with sharp gradient in dust density, very similar to those found in numerical solutions of the fully nonlinear fluid equations for...