Infinitely many multipulse solitons of different symmetry types in the nonlinear Schrodinger equation with quartic dispersion

We show that the generalized nonlinear Schrodinger 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 traveling 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 waveguides over several dispersion lengths.

Automated summary

The study reveals that the generalized nonlinear Schrodinger equation with quartic dispersion supports infinitely many multipulse solitons in infinite families with different signatures. By studying reduced systems and families of connecting orbits with different symmetry properties, the overall structure of solitons can be understood.