Mechanics

On Rationally Complete Algebraic Systems of Finite Strain Tensors of Complex Continua

Authors: Kovalev V. A., Radaev Y. N.

The paper is devoted to the mathematical description of complex continua and the systematic derivation of strain tensors by the notion of isometric immersion of complex continuum in a plane space of higher dimension. Problem of establishing of complete systems of irreducible objective strain and extra-strain tensors for complex continuum immersed in an external plane space is considered. The solution to the problem is given by methods of the field theory and the theory of algebraic invariants.

Exact Solitary-wave Solutions of the Burgers – Huxley and Bradley – Harper Equations

Authors: Zemlyanukhin A. I., Bochkarev A. V.

It is shown that the exact soliton-like solutions of nonlinear wave mechanics evolution equations can be obtained by direct perturbation method based on the solution of a linearized equation. The sought solutions are sums of the perturbation series which can be found using the requirement that the series are to be geometric. This requirement leads to the conditions for the coefficients of the equations and parameters of the sought solutions.