Alexander F. Vakakis is an associate professor in the Department of Mechanical and Industrial Engineering of the University of Illinois at Urbana-Champaign. His research interests include linear and nonlinear dynamics and vibrations, modal analysis, structural wave propagation, and bioengineering. He is an NSF Young Investigator Award recipient (1994), and his research is supported by federal and industrial grants. He received his Ph D from the California Institute of Technology in 1990. Leonid I. Manevitch is a professor in the Institute of Chemical Physics at the Russian Academy of Sciences, Moscow. He has published numerous papers and books on nonlinear dynamics and its applications. His current research interests center on nonlinear phenomena in molecular dynamics. Yuri V. Mikhlin is a professor in the Department of Applied Mathematics at Kharkov”s Polytechnic University in the Ukraine. He received his doctor of science degree from the Institute of Mechanical Problems at the Russian Academy of Sciences. His current research focuses on nonlinear oscillations of conservative and vibro-impact systems and on nonlinear solitary waves. Valery N. Pilipchuk is a professor and Head of the Department of Applied Mathematics at the Ukrainian State Chemical and Technological University, Dnepropetrovsk, Ukraine. He received his two doctor of science degrees from the Institute of Mechanical Problems at the Russian Academy of Sciences in 1992. His research interests include nonlinear oscillations and waves and the theory of ordinary differential equations. Alexandr A. Zevin is a researcher at the Transmag Research Institute at the Ukrainian Academy of Sciences, Dnepropetrovsk, Ukraine. He received his doctor of science degree from the Institute of Mechanical Problems at the Russian Academy of Sciences in 1989. His current research interests include the qualitative theory of nonlinear oscillations, and the theory of nonlinear ordinary differential equations.