  In this work, the emergence of single-peak temporal dissipative solitons in
singly-resonant degenerate optical parametric oscillators is investigated
analytically. Applying the Kantarovich optimization method, through a
Lagrangian variational formalism, an approximate analytical soliton solution is
computed using a parameter-dependent ansatz. This permits to obtain analytical
estimations for the dissipative soliton energy, peak power, and existence
boundaries, which are of great value for experimentalist. To confirm the
validity of this procedure, these analytical results are compared with a
numerical study performed in the context of pure quadratic systems, showing a
good agreement.
