As demand for ocean energy conversion systems and marine vehicles and structures has increased in recent decades, the wave environments these systems operate in have become increasingly challenging. In particular, ocean waves can exhibit highly nonlinear and extreme behavior. In this presentation, we introduce modern nonlinear models of waves and ocean systems, together with mathematical methods for characterizing their dynamics and coupled behavior under both deep- and shallow-water conditions. Specifically, the Kadomtsev–Petviashvili (KP), Korteweg–de Vries (KdV), and nonlinear Schrödinger (NLS) equations are used to model nonlinear wave fields, while nonlinear beam and plate models are employed to describe structural responses. Our models are formulated within the Hamiltonian framework of classical mechanics, which provides a systematic basis for incorporating higher-order correction terms into the physical models and for connecting ocean engineering problems with recent advances in mathematical physics. This research is motivated by the analysis of elastic vibrations of marine structures and hydrofoils induced by nonlinear waves. Of particular interest is the focusing NLS equation, which is completely integrable and can therefore be solved using the inverse scattering transform. This framework enables coherent structures to be parameterized explicitly and provides a theory of exact analytical solutions. Building on these methods, we develop an explicit analytical nonlinear solution for the response of structural systems to random wave excitation, with consistent levels of nonlinearity represented in both the input wave field and the structural response. Together, these approaches provide a unified framework for understanding and predicting the coupled nonlinear behavior of waves and marine structures.
Beyer Distinguished Lecture Series
Analytical Time- and Spatial-Domain Solutions of Nonlinear Ocean Waves and Hamiltonian Dynamical System Response
Speaker
Solomon Yim
Date
Location
CBB 118
Abstract
About the speaker
: Dr. Solomon C. Yim is Professor of Coastal & Ocean and Structural Engineering at Oregon State University (OSU). He received his BS in Civil Engineering from Rice University and his MS and PhD in Structural Engineering and MA in Mathematics from the University of California, Berkeley. Prior to joining OSU, he was a Senior Research Engineer at Exxon Production Research Company in Houston, Texas. Dr. Yim has received sustained research support throughout his career from the Office of Naval Research, Naval Facilities Engineering Systems Command, U.S. Department of Energy, and National Science Foundation. He has held several leadership positions at OSU, including Inaugural G.W. Holcomb Professor of Structural Engineering, Director of the Transportation Research Institute, and Interim Director of the Hinsdale Wave Research Laboratory. He has led major, multi-year initiatives in large-scale experimental research, including the NSF-funded Tsunami Research Center wave basins and Tsunami Research Facilities Operations program. He has also played a key role in the development of the Northwest National Marine Renewable Energy Center and the Pacific Marine Energy Center, contributing to research and development in wave energy conversion since the early 2000s. Dr. Yim is a Fellow of the American Society of Mechanical Engineers and the American Society of Civil Engineers. His numerous honors include the U.S. Navy Senior Faculty Research Fellowship, Royal Norwegian Research Council Senior Visiting Scientist Award, OSU College of Engineering Research Leadership Award, Network for Earthquake Engineering Simulation Best Research Project Award, and the 2026 OMAE Conference Renewable Energy Symposium Best Paper Award. He has also held several major leadership and editorial positions in the ASME Ocean, Offshore and Arctic Engineering Division and has received multiple division awards for distinguished service and research achievement.