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

Infinitely Many Multipulse Solitons of Different Symmetry Types in the Nonlinear Schr\"{o}dinger Equation with Quartic Dispersion