  We show that the generalised nonlinear Schr\"{o}dinger equation (GNLSE) with
quartic dispersion supports infinitely many multipulse solitons for a wide
parameter range of the dispersion terms. These solitons exist through the
balance between the quartic and quadratic dispersions with the Kerr
nonlinearity, and they come in infinite families with different signatures. A
travelling wave ansatz, where the optical pulse does not undergo a change in
shape while propagating, allows us to transform the GNLSE into a fourth-order
nonlinear Hamiltonian ordinary differential equation with two reversibilities.
Studying families of connecting orbits with different symmetry properties of
this reduced system, connecting equilibria to themselves or to periodic
solutions, provides the key to understanding the overall structure of solitons
of the GNLSE. Integrating a perturbation of them as solutions of the GNLSE
suggests that some of these solitons may be observable experimentally in
photonic crystal wave-guides over several dispersion lengths.
