相关论文: On exact solutions of nonlinear acoustic equations

We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…

A new set of nonlinear coupled equations is derived in the context of small amplitude limit of the general wave equations in a fluid type warm electrons/cold ions plasma irradiated by a continuous laser beam. This limit is proved to be…

Magnetosonic waves are intensively studied due to their importance in space plasmas and also in fusion plasmas where they are used in particle acceleration and heating experiments. In the present paper we investigate the magnetosonic waves…

In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a…

Practical application of Gauss' law in acoustics is not a very well known method. However, any inverse square law behavior can be formulated in the way similar to Gauss' law, which allows us to extend the same principle to sound waves…

This paper is concerned with the spatial propagation of nonlocal dispersal equations with bistable or multistable nonlinearity in exterior domains. We obtain the existence and uniqueness of an entire solution which behaves like a planar…

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. Exact solution with own angular momentum in form of a…

The narrow and wide-angle parabolic equations for the quasi-monochromatic sound wave packets propagating in a waveguide with a non-stationary background flow are obtained. The results of numerical simulations are presented.

The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with…

We consider in the unidirectional approximation the propagation of an ultra short electromagnetic pulse in a resonant medium consisting of molecules characterized by a transition operator with both diagonal and non-diagonal matrix elements.…

We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.

Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant…

Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…

This work is concerned with the broad question of propagation of regularity for smooth solutions to non-linear Vlasov equations. For a class of equations (that includes Vlasov-Poisson and relativistic Vlasov-Maxwell), we prove that higher…

The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…

Nonlinear ion-acoustic waves are analyzed in a non-relativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary…

It is shown that incompressible spin quantum Hall magnetohydrodynamics allows an exact solution for the propagation of a circularly polarized electromagnetic wave. The solution is obtained assuming a condition between the fluid velocity and…

Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…

We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order…

A modelling of low-frequency sound propagation in slowly varying ducts with smoothly varying lining is proposed leading to an acoustic mild-slope equation analogue to the with mild-slope equation for water waves. This simple 1D Mild Slope…