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We study the dynamical behaviors of a system of five coupled nonlinear equations that describes the dynamics of acoustic-gravity waves in the atmosphere. A linear stability analysis together with the analysis of Lyapunov exponents spectra…
We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear…
A numerical study of fractional Camassa-Holm equations is presented. Smooth solitary waves are constructed numerically. Their stability is studied as well as the long time behavior of solutions for general localised initial data from the…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
We investigate the conditions for the emergence of wave instabilities in a vacuum cavity delimited by cylindrical metallic walls under rotation. It is shown that for a small vacuum gap and for an angular velocity exceeding a certain…
We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently thin fluid layers the surface is…
The generalized Levy-Leblond equation for a $(3+1)$-dimensional self-interacting Fermi field is considered. Spin up solitary wave solutions with space oscillations in the $x^3$-coordinate are constructed. The solutions are shown to…
Propagation of weak gravitational waves, when a dynamical four-form is around, has been investigated. Exact, self-consistent solutions corresponding to plane, monochromatic gravitational waves have been studied.
The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional…
Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
This work is devoted to study the dynamics of the supercritical gKDV equations near solitary waves in the energy space $H^1$. We construct smooth local center-stable, center-unstable and center manifolds near the manifold of solitary waves…
We consider perturbations of the one-dimensional cubic Schr\"odinger equation, under the form $i \, \partial_t \psi + \partial_x^2 \psi + |\psi|^2 \psi - g( |\psi|^2 ) \psi = 0$. Under hypotheses on the function g that can be easily…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
A method is proposed for finding the wave field components which are weakly sensitive to the sound speed perturbation in the ocean acoustic waveguides. Such a component is formed by a narrow beam of rays whose spread in vertical direction,…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density…
The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…