We explore variational Poisson–Nijenhuis structures on nonlinear PDEs and establish relations between Schouten and Nijenhuis brackets on the initial equation with the Lie bracket of symmetries on its natural extensions (coverings). This approach allows to construct a framework for the theory of nonlocal structures.
The features of neural networks using for increasing of an accuracy of physical quantity measurement are considered by prediction of sensor drift. The technique of data volume increasing for predicting neural network training is offered at the expense of various data types replacement for neural network training and at the expense of the separate… (More)
Using geometrical approach exposed in Refs. [12, 13], we explore the Camassa– Holm equation (both in its initial scalar form, and in the form of 2 × 2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).