Given a closed, connected, symplectic manifold $(X^{2n},\omega)$, is there a systematic method to computing the Poincaré dual surface to degree $(2n-2)$ classes of the form
$$[\omega]^{n-2}\cup B + \lambda [\omega]^{n-1}$$
where $B$ is a primitive degree $2$ class, and $\lambda$ is any real scalar? If there are only ad hoc methods, do any of you have any good sources I could go chasing? What are some basic considerations I should have when doing this computation?