Some aspects of self-duality and generalised BPS theories

If a scalar eld theory in (1+1) dimensions possesses soliton solutions obeying rst order BPS equations, then, in general, it is possible to nd an in nite number of related eld theories with BPS solitons which obey closely related BPS equations. We point out that this fact may be understood as a simple consequence of an appropriately generalised notion of self-duality. We show that this self-duality framework enables us to generalize to higher dimensions the construction of new solitons from already known solutions. By performing simple eld transformations our procedure allows us to relate solitons with di erent topological properties. We present several interesting examples of such solitons in two and three dimensions.