Quasi-periodic shape-transformations of nonlocal higher-order solitons

Quasiperiodic oscillations and transverse shape-transformations of higher-order bright solitons in nonlinear nonlocal media have been frequently observed in recent years, however, the origin of these phenomena was never completely elucidated. In this work, we perform a linear stability analysis of these higher-order solitons by solving the Bogoliubov-de Gennes equations numerically. This enables us to understand the emergence of a new oscillatory state as a growing unstable mode of a higher-order soliton. Using dynamically important states as a basis, we provide low-dimensional visualizations of the dynamics and identify quasiperiodic and homoclinic orbits, linking the latter to shape-transformations.