Skew-symmetric forms: On integrability of equations of mathematical physics http://arxiv.org/abs/0910.5849статья

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[1] Petrova L. I. Skew-symmetric forms: On integrability of equations of mathematical physics http://arxiv.org/abs/0910.5849 // ArXiv e-prints. — 2009. — P. 1–8. Submitted on 30 The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived from these equations. Such a relation connects the differential of state functional and the skew-symmetric form. This relation proves to be nonidentical, and this fact points to the nonintegrability of the equations. In this case a solution to the equations is a functional, which depends on the commutator of skew-symmetric form that appears to be unclosed. However, under realization of the conditions of degenerate transformations, from the nonidentical relation it follows the identical one on some structure. This points out to the local integrability and realization of a generalized solution. In doing so, in addition to the exterior forms, the skew-symmetric forms, which, in contrast to exterior forms, are defined on nonintegrable manifolds (such as tangent manifolds of differential equations, Lagrangian manifolds and so on), were used.

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