On the variational form of evolution equations

In this paper a new definition is given for representability in the form of a variational derivative; a particular case of this definition yields the classical expression for the variational derivative. A close connection will be demonstrated between the variational derivative and the exterior differentiation operator d. For the case of functions of one variable one obtains effective computational criteria which solve the “hidden variability” problem. The rigorous mathematical theory is illustrated as applied to the study of a few nonlinear equations of mathematical physics.