Instanton chains with soliton limits

It is well known that the Yang-Mills instanton equations in R⁴ may be reduced to the static monopole equation in R³, by requiring the gauge potential to be independent of one coordinate. Furthermore, the static monopole solution may be obtained from an instanton chain in the limit in which the number of instantons becomes infinite. In this letter we point out that there is a simple lower dimensional analogue of this result. By requiring the gauge potential of the CP¹ s-model in R² to be independent of one coordinate, the static sine-Gordon equation in R may be obtained. Furthermore, the sine-Gordon soliton solution may be constructed from a CP¹ instanton chain in the limit in which the instanton number becomes infinite.