Related papers: On a wave equation with singular dissipation
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a…
We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
In this paper, we consider the Cauchy problem for a non-homogeneous wave equation generated by the fractional Laplacian and involving different kinds of lower order terms. We allow the equation coefficients and data to be of distributional…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…
We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider…
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the…
We consider an extension of the kinetic equation developed by Newell & Zakharov (A.C. Newell and V.E. Zakharov. The role of the generalized Phillips' spectrum in wave turbulence. Phys.Lett.A, 372:4230-4233, 2008). The new equation takes…
At singular points of a wave field, where the amplitude vanishes, the phase may become singular and wavefront dislocation may occur. In this Letter, we investigate for wave fields in one spatial dimension the appearance of these essentially…
The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…
Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence: the mutual…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…
We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier; the space-homogeneous case is a simple variant. We determine…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
In this paper, we study the large time behavior of a class of wave equation with a nonlinear dissipation in non-cylindrical domains. The result we obtained here relaxes the conditions for the nonlinear term coefficients (in precise, that is…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…