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

TL;DR

This paper demonstrates that the generalized nonlinear Schrödinger equation with quartic dispersion admits infinitely many multipulse solitons of various symmetries, expanding understanding of complex wave solutions in nonlinear optics.

Contribution

It introduces a novel analysis of the GNLSE with quartic dispersion, revealing infinite families of multipulse solitons with different symmetry properties and potential experimental observability.

Findings

Existence of infinitely many multipulse solitons with different symmetries.

Reduction of GNLSE to a fourth-order nonlinear Hamiltonian ODE.

Potential for experimental observation in photonic crystal waveguides.

Abstract

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.