Related papers: Amplitude modulated drift wave packets in a nonuni…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
The nonlinear dynamics of circularly polarized dispersive Alfv{\'e}n wave (AW) envelopes coupled to the driven ion sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number…
We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of…
We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma,…
We study the dynamics of an electron wave packet in a strong constant crossed electromagnetic field with account for radiative corrections due to interaction of the electron with the vacuum fluctuations. We evaluate a wave packet composed…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
The nonlinear coupling between the light beams and non-resonant ion density perturbations in a plasma is considered, taking into account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations…
We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation.…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…
Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schr\"odinger equation we will introduce a transformation to displaced…
We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a…
We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped…
The existence of a dispersion-managed soliton in two-dimensional nonlinear Schr\"odinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully…
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena…
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an…
By employing a local two-fluid theory, we investigate an obliquely propagating electromagnetic instability in the lower hybrid frequency range driven by cross-field current or relative drifts between electrons and ions. The theory…
Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By…
The stability and dynamical properties of the so-called resonant nonlinear Schr\"odinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schr\"odinger (NLS) equation with the addition of a perturbation used to…