Optical solitons are wave packets of light, with the distinctive property of being unchanging as they propagate. Optical solitons form from the balance between linear dispersion effects and the nonlinear Kerr effect, with research historically focused on modifying the nonlinearity. However, new experimental results reveal novel soliton solutions, most notably the pure quartic dispersion soliton, emerging from changes to the dispersion instead. Conventional soliton solutions were limited to quadratic dispersion, but new results showed that higher order even dispersion effects would allow similar, unchanging soliton pulses to form. In this work, we present a categorisation of 6th order dispersion soliton solutions using the analytic tail approach. We identify that the majority of bright soliton solutions at higher order dispersion fall into one of two categorisations, solutions with oscillating exponential or purely exponential tails. A contraction of the higher order dispersion solution space was achieved, allowing us to draw conclusions about the larger space using these different categories. Our work continued into the search for exact analytic soliton solutions in this higher order dispersion space, using two approaches. The first uncovered families of soliton solutions with purely exponential tails, at arbitrary dispersion order, taking the form of powers of hyperbolic secants and sums thereof. This approach started with the analytic form of the solution and then found the associated equation. In the second approach, we developed a systematic iterative method, requiring no initial assumptions, generating analytic series solutions. This method significantly broadens the scope of analytic solutions we could obtain, as the method is able to generate solutions for the majority of solitons with oscillating decaying tails. Using this method, we generated the analytic series form of the pure quartic soliton, and a number of other higher order dispersion solutions.