Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation

Abstract

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.

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• A nonlocal variable coefficient modified KdV equation derived from two-layer fluid system and its exact solutions
• A nonlocal nonlinear Schrodinger equation derived from a two-layer fluid model