Showing papers by "Alexander M. Samsonov published in 1995"

Long non-linear strain waves in layered elastic half-space

Abstract: Elastic strain wave propagation in a thin non-linearly elastic layer superimposed on non-linearly elastic half-space is studied. Two layer-half-space contact models are considered. It is found that the Benjamin-Ono equation can be derived for description of longitudinal non-linear strain waves, when the contact between the layer and the half-space is provided only by means of the normal stresses and displacements. When the full contact problem is considered the more complicated integro-differential equation is derived. It is found that long non-linear periodical and solitary strain waves as well as envelope waves may exist in the first case, while only envelope wave solutions are found to the full contact problem. Linear wave analysis shows that the Korteveg-de Vries equation, often usable, is unlikely to be an adequate model for longitudinal surface strain waves. Application of the results obtained to experiments devoted to superconductivity threshold control in thin metal films as well as to generation of acoustic solitons in layered half-space is discussed.

Travelling wave solutions for nonlinear dispersive equations with dissipation

Abstract: It is shown that in order to obtain travelling wave solution many nonlinear dispersive equations with dissipative terms can be reduced by means of elementary transformations to the 1st order Abel o.d.e., and consequently, to the Emden-Fowler equation, if both nonlinear and dissipative terms are polynomials. These reductions can be integrated in closed form in terms of the Weierstrass elliptic function p, containing kink solutions as appropriate limits. Additional conditions for the equation coefficients and wave parameters are established for the wave existence, and their physical meaning is analysed. Some of nonlinear o.d.e., particularly, of higher order, do not provide a reduction to the Abel equation, therefore a different algorithm is proposed to obtain some exact solutions in terms of elliptic p-function.