10 citations · 19 across the 5 of their papers we have counts for
6 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…
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…
A new method for solving completely integrable PDEs
Andrey Melnikov
The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV),…
Overdetermined conservative 2D Systems, Invariant in One Direction and a Generalization of Potapov's theorem
Andrey Melnikov, Victor Vinnikov
This work is a direct continuation of the authors work arXiv:0812.3779v1. A special case of conservative overdetermined time invariant 2D systems is developed and studied. Defining…
Overdetermined 2D Systems Invariant in One Direction and Their Transfer Functions
Andrey Melnikov, Victor Vinnikov
In this work we develop a theory of Vessels. This object arises in the study of overdetermined 2D systems invariant in one of the variables, which are usually called time invariant…