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On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the…
The nonlinear evolution of a unstable electrostatic wave is considered for a multi-species Vlasov plasma. From the singularity structure of the associated amplitude expansions, the asymptotic features of the electric field and distribution…
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 present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed…
Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out…
In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and…
In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…
In this paper we present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary…
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 atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and…
We present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, non-linearly to the field strength. We work in the context of Maxwell' s theory in the low frequency limit and…
The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney--Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances…
Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes,…
We analyze relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to the wave-packet…
This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…
We consider the periodic solutions of a semilinear variable coefficient wave equation arising from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The variable coefficient…
A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic…