10 citations · 59 across the 16 of their papers we have counts for
16 papers
On the extended use of Backus average
Andrey Melnikov
Backus (1962) developed his technique for homogenization of a layered structure solely within the context of linear elastic theory. In this paper we propose an extended use of Back…
On deformation-gradient tensors as two-point tensors in curvilinear coordinates
Andrey Melnikov, Michael A. Slawinski
We derive a general expression for the deformation-gradient tensor by invoking the standard definition of a gradient of a vector field in curvilinear coordinates. This expression s…
Classification of KdV vessels with constant parameters and two dimensional outer space
Andrey Melnikov
In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \textit{unified} approach for them. The classification includes such import…
Inverse scattering of Canonical systems and their evolution
Andrey Melnikov
In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficie…
Solution of the KdV equation on the line with analytic initial potential
Andrey Melnikov
We present a theory of Sturm-Liouville non-symmetric vessels, realizing an inverse scattering theory for the Sturm-Liouville operator with analytic potentials on the line. This con…
Solution of the Boussinesq equation using evolutionary vessels
Andrey Melnikov
In this work we present a solution of the Boussinesq equation. The derived formulas include solitons, Schwartz class solutions and solutions, possessing singularities on a closed s…