In the symmetric double well potential, the solutions in $1+1$ static and real $\varphi^4$ theory, are solitons. However, we know that such theories are "dual" to one dimensional real $\varphi^4$ theories, and solutions of those after Wick rotation are instantons, also they have same mathematical form of solitons.
My question is, is this soliton-instanton correspondence just a special case? or applicable to any potential of those dual theories? More generally, Is every soliton has corresponding instanton after Wick rotation?