Propagators for non-linear systems

A canonical formalism based on forward and backward propagators is developed for problems described by systems of general non-linear equations. These propagators are shown to yield the problem's solution by propagating exactly the bulk/surface/initial sources. They naturally generalise to non-linear problems the Green functions of linear theory. Unlike the customary Green functions, though, the forward and backward propagators depend parametrically and non-linearly on the problem's solution; however, the propagators themselves satisfy linear equations that can, in principle, be solved by methods of linear theory. Three examples, comprising both scalar and vector problems, are presented to highlight the main points underlying the application of this formalism.