Kenji Nakanishi

Schlumberger Chair for Mathematical Sciences

Mathematician Kenji Nakanishi studies nonlinear wave equations to understand how phenomena such as solitons, scattering, and blow-up emerge and evolve.

Kenji Nakanishi is a professor at the Research Institute for Mathematical Sciences at Kyoto University. He earned both his master’s and doctoral degrees in mathematical sciences from the University of Tokyo before pursuing his academic career in Kyoto. His research focuses primarily on the mathematical analysis of partial differential equations, particularly nonlinear wave and dispersive equations, which describe the evolution of waves subject to strong interactions.

He is particularly interested in how these equations can produce very different behaviors depending on the balance between dispersion and nonlinear interactions. A single equation can give rise to phenomena such as wave scattering, the formation of solitons — structures that propagate without changing shape — or the blow-up of a solution in finite time. Such questions arise in a variety of physical settings, including plasmas, superfluids, and water waves.

A major part of his work seeks to understand the global dynamics of these systems: rather than studying an isolated solution, he aims to describe the full range of possible behaviors and the transitions between them. He has studied, in particular, the dynamics around solitons and phenomena that occur when the energy of a system lies near critical thresholds. His research thus combines analysis, geometry, and dynamical systems theory to build a broader picture of the possible behaviors of nonlinear wave systems.

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