  Quasiperiodic oscillations and 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 paper, we perform a linear stability analysis of these higher-order
solitons by solving the Bogoliubov-de Gennes equations. 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.
