  Dark solitons are common topological excitations in a wide array of nonlinear
waves. The dark soliton excitation energy, crucial for exploring dark soliton
dynamics, is necessarily calculated in a renormalized form due to its existence
on a finite background. Despite its tremendous importance and success, the
renormalized energy form was firstly only suggested with no detailed
derivation, and was then "derived" in the grand canonical ensemble. In this
work, we revisit this fundamental problem and provide an alternative and
intuitive derivation of the energy form from the fundamental field energy by
utilizing a limiting procedure that conserves number of particles. Our
derivation yields the same result, putting therefore the dark soliton energy
form on a solid basis.
