Weak Interactions of Solitary Waves in Generalized NLS Equations, Part II

Weak Interactions of Solitary Waves in Generalized NLS Equations, Part II

Yi Zhu
Department of Applied Mathematics
University of Colorado at Boulder

In this talk, the ODE system which governs the dynamics of weak interactions of solitary waves in generalized NLS equations is analyzed comprehensively. Using asymptotic methods along separatrix orbits, a simple second-order map is derived. This map does not have any free parameters after variable rescalings, and thus is universal for all weak solitary-wave interactions in generalized NLS equations. Comparison between this map's predictions and direct simulations of the ODE system shows that the map can capture the fractal-scattering phenomenon of the ODE system very well both qualitatively and quantitatively.