Abstract
A precise meaning is given to the idea of a kink theory approximating a vectoror vector-bundle-valued theory. It is shown that vector theories taking values in a vector bundle with groupSO(n-s,s;ℝ), acting naturally, do not approximate any kink theory. It is further shown that, where a kink theory is approximated by a vector bundle theory, the field equations in the vector theory can give rise to field equations in the kink theory. The theory of Skyrme and the sine-Gordon theory are of this form. An example is given of a nonlinear modification of electromagnetism having solitonlike solutions.
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