Wave Propagation in Dissipative or Dispersive Non-linear Media

Mixed nonlinearity and double shocks in superfluid helium

“…Furthermore, certain terms neglected, and therefore not shown, in (A 2 ) will make contributions equal to that of the quadratic term shown. Teymur & Suhubi (1978) have presented a method of accounting for the higherorder terms when the speed matrix A , is of special form. However, the required conditions are not satisfied in general problems and, in particular, the superfluid system.…”

“…when & = O ( 1 ) and the & = 0 extension by Teymur & Suhubi (1978) can be applied to a restricted class of problems, no general techniques are available when (1.4) holds. In response to this, the present authors have developed a general extension of the technique of Taniuti & Wei and apply it to He 11.…”

Asymptotic solution of a non-linear wave motion in an electron plasma

“…Physically, we deal with the propagation of non-linear waves in a cylindrically symmetric flow of a hot-electron plasma in the absence of a magnetic field. The governing partial differential equations of such a radial flow exterior to the cylindrical surface of the line source can be written in the following from [10]:…”

“…Several methods of approach to investigate the asymptotic properties of non-linear waves have been developed in the literature [4,9,10]. The literature also offers several physical examples of non-linear media represented by a hyperbolic system of quasi-linear partial differential equations, which are compatible under different kinds of approximations and exhibit wave processes asymptotically described by transport equations [12].…”

Nonlinear wave motion governed by the modified Burgers equation

“…Our assumption is here that the dominant mechanism has the nature of a viscosity, leading to a second derivative in the evolution equation for a unidirectional wave, which would then be of the form in which all variables are dimensionless, X is a range variable and r a retarded time, or linear phase variable. Certain representations o f viscoelastic solid behaviour do indeed lead to an equation of the form (1.1), as was first shown by Nariboli & Lin (1973) and subsequently by Teymur & Suhubi (1978). Nariboli & Lin also show the applicability of (1.1) to the problem of magnetohydrodynamic 'switch-on' shock waves, whereas a generalized version of (1.1), including linear terms representing dispersion and ray-tube area change, was shown by Gorschkov et al (1974) to describe the electric field in a nonlinear isotropic dielectric (V then referring either to the axial electric field or the azimuthal magnetic field in a cylindrically diverging electromagnetic field).…”