We consider a two-component, two-dimensional nonlinear Schr¨odinger system with unequal dispersion coefficients and self-defocusing nonlinearities. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component. We show that the potential well may support not only the fundamental bound state, which forms a vortex–bright (VB) soliton, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution in the case examples considered leads to transformation of the multi-ring complexes into stable VB soliton ones with the fundamental state in the second component.
Charalampidis, E. G.; Kevrekidis, Panayotis G.; Frantzeskakis, D. J.; and Malomed, B. A., "Vortex–Soliton Complexes in Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients" (2015). Mathematics and Statistics Department Faculty Publication Series. 1214.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1214