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Nakanishi Lab
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The lab mathematically analyzes nonlinear wave equations.
AboutAbout the lab
Uncovering the behavior of waves through equations.
The Nakanishi Lab studies the mathematical analysis of partial differential equations.
Its main subjects are nonlinear partial differential equations describing the spatiotemporal evolution of strongly interacting waves, such as those in plasmas, water surface waves, superfluids, and optical fibers.
A variety of time evolutions arise from the competition between the dispersion of waves and nonlinear interaction.
Recently, aiming to capture the behavior of general solutions as a whole, the lab has been investigating transitions between typical behaviors, as well as intermediate states.
Key terms
- Partial differential equation
- An equation expressing the relationship between a function of several variables and its rates of change. It describes, for example, how waves propagate
- Dispersion
- The property that waves of different wavelengths travel at different speeds, so that a wave spreads out over time
- Soliton
- An isolated wave that travels without changing its shape. It appears as a solution of nonlinear equations
ResearchResearch themes
The lab studies the mathematical analysis of partial differential equations, especially equations known as nonlinear wave equations and nonlinear dispersive equations. It investigates the global-in-time behavior of solutions from two sides: developing techniques and elucidating phenomena.
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MembersFaculty
- ProfessorKenji Nakanishi
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Korteweg-de Vries equation for solitons” Diederik Korteweg. Gustav de Vries. Sander Bais. Gijs Mathijs Ontwerpers, Amsterdam / Public domain (cropped)
- Analysis of Nonlinear Dispersive Equations: “Rogue wave (01)” Collège Beauvoir / CC BY 4.0 (cropped)
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