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Expansions in the oscillation modes of tidally perturbed bodies provide a useful framework for representing tidally induced flows. However, recent work has demonstrated that such expansions produce inaccurate predictions for secular orbital…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
The formation of thermoacoustic shocks is studied in a fluid complex plasma. The thermoacoustic wave mode can be damped (or anti-damped) when the contribution from the thermoacoustic interaction is lower (or higher) than that due to the…
Collisional relaxation of Coulomb systems is studied in the strongly coupled regime. We use an optical pump-probe approach to manipulate and monitor the dynamics of ions in an ultracold neutral plasma, which allows direct measurement of…
Using high resolution Vlasov - Poisson simulations, evolution of driven ``cold" electron plasma wave (EPW) in the presence of stationary inhomogeneous background of ions is studied. Mode coupling dynamics between ``cold'' EPW with phase…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when…
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently…
The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric…
Slow magnetoacoustic waves represent an important tool for probing the solar coronal plasma. We quantitatively assess the applicability of the weak thermal conduction theory to coronal seismology by slow waves. We numerically model the…
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics.…
Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…
A new technique for manipulation and control of gradient-driven instabilities through nonlinear interaction with Alfv\'en waves in a laboratory plasma is presented. A narrow field-aligned density depletion is created in the Large Plasma…