  We study solitary wave solutions for the nonlinear Schr\"odinger equation
perturbed by the effects of third-, and fourth-order dispersion, maintaining a
wavenumber gap between the solitary waves and the propagation constant. We
numerically construct members of a family of such solitary waves, including
Kruglov and Harvey's exact solution, using the spectral renormalization method
and establish empirical relations between the pulse parameters. A deeper
insight into the properties of solitary waves and solitons can be obtained
through collisions. Therefore we perform pulse propagation simulations
demonstrating different collision regimes. Depending on the pulses initial
phase difference, this can lead to the formation of short-lived two-pulse bound
states. While these collisions are generally inelastic, singular phase values
exist at which they are elastic. Finally, we detail the properties of Kruglov
and Harvey's soliton solution under loss, verifying earlier predictions of
perturbation theory and suggesting a convergence to the soliton solution of the
standard nonlinear Schr\"odinger equation in the limit of large propagation
distances.
