A generalization of the classical Leray – Schauder fixed point theorem, based on the infinite-dimensional Borsuk – Ulam type antipode construction, is proposed. A new nonstandard proof of the classical Leray – Schauder ...

The differential-geometric aspects of generalized de Rham – Hodge complexes naturally related with integrable multidimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic ...

The Lax integrability of a two-component polynomial Burgers-type dynamical system is analyzed by using a differential-algebraic approach. Its linear adjoint matrix Lax representation is constructed. A related recursive ...

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The ...

Backgrounds of a new mathematical physics discipline ’Quantum Mathematics’ are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented ...

We study swept-volume dynamical systems for which several hydrodynamical models are formulated. The properties of those hydrodynamical models are studied by means of the algebraic Kostant – Symes technique. A differentia ...

The canonical reduction method is analized in detail and applied to Maxwell and Yang– Mills equations considered as Hamiltonian systems on some fiber bundles with symplectic and connection structures. The minimum interaction ...

The work is devoted to the study of the Lagrangian and Hamiltonian properties of some relativistic electrodynamics models and is a continuation of our previous investigations. Based on the vacuum field theory approach, ...

We study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra G=K⊕P, where K is the Lie algebra of a fixed ...