Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation

Abstract

Quasiperiodic oscillations and shape-transformations of higher-order bright\nsolitons in nonlinear nonlocal media have been frequently observed in recent\nyears, however, the origin of these phenomena was never completely elucidated.\nIn this paper, we perform a linear stability analysis of these higher-order\nsolitons by solving the Bogoliubov-de Gennes equations. This enables us to\nunderstand the emergence of a new oscillatory state as a growing unstable mode\nof a higher-order soliton. Using dynamically important states as a basis, we\nprovide low-dimensional visualizations of the dynamics and identify\nquasiperiodic and homoclinic orbits, linking the latter to\nshape-transformations.\n