LAWRENCE—Milena Stanislavova’s, professor of mathematics and chair of economics, and Atanas Stefanov’s, professor of mathematics, recent paper Asymptotic stability for spectrally stable Lugiato-Lefever solitons in periodic waveguideswas featured on the cover of the October 2018 issue of the Journal of Mathematical Physics and was chosen as an editor’s pick. The paper was also highlighted by the American Institute of Physics publishing house Scilight.
The Scilight article mentions Stanislavova’s and Stefanov’s work to investigate the asymptotic stability of spectrally stable periodic solutions of the Lugiato-Lefever equation. The Lugiato-Lefever equation, derived over 30 years ago, provides a model to describe spontaneous pattern formation in the field of nonlinear fiber optics. It describes the generation of Kerr frequency combs that have numerous potential applications in high-capacity telecommunications, chemical sensing, astronomy and more.The existence of such solutions was recently established, which is of significant practical interest since they correspond to stable Kerr frequency combs. The authors wanted to confirm the longtime behavior of these steady states by delving into a rigorous mathematical proof. In the end, the authors showed that spectrally stable periodic waves for the Lugiato-Lefever model are nonlinearly stable. Their contribution consists of the rigorous proof that describes the behavior of the system. The work has the potential to highlight new features of the model that haven’t been observed yet and to possibly suggest new experiments that may be conducted.
Stanislavova’s research interests are in dynamical systems, nonlinear partial differential equations and semigroups of linear operators. Her work is supported by the National Science Foundation. She received her doctorate in 2000 from the University of Missouri. Before coming to KU in 2002, she held a visiting position at the University of Massachusetts. She is currently chair of the Economics Department.
Stefanov’s research interests are in soliton dynamics, nonlinear dispersive partial differential equations, and solitary waves. His work is supported by the National Science Foundation. He received his doctorate in 1999 from the University of Missouri and held a visiting position at the University of Massachusetts before coming to KU in 2002. He received KU’s Scholarly Achievement Award in 2015.