Related papers: Degenerate weakly nonlinear elastic plane waves
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial is considered. If the group velocities dispersion is not taken into account, then wave propagation can be described either by the…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
Propagation of the finite amplitude electromagnetic wave through the partially spin-polarized degenerate plasmas leads to the instability. The instability happens at the interaction of the electromagnetic wave with the small frequency…
Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system…
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.
Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide…
The wave propagation problem on a taut cable resting on a bilinear substrate is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to permit…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schr{\"o}dinger-like equations. The…
The nonlinear propagation of small amplitude ion acoustic solitary wave in relativistic degenerate magneto plasma in presence of ion beam is investigated in detail. The nonlinear equations describing the evolution of solitary wave in…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and…
Propagation of extremely short unipolar pulses of electromagnetic field ("videopulses") is considered in the framework of a model in which the material medium is represented by anharmonic oscillators (approximating bound electrons) with…
We consider a degenerate wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
We study the propagation of sound waves in a three-dimensional, infinite ambient flow with weak random fluctuations of the mean particle velocity and speed of sound. We more particularly address the regime where the acoustic wavelengths are…
In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the…