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Partial Differential Equations Lab (Tomoyuki Tanaka)
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The lab studies the existence and behavior of solutions to nonlinear partial differential equations related to wave phenomena.
AboutAbout the lab
Exploring what the solutions to wave equations look like.
Associate Professor Tomoyuki Tanaka, who works on the theory of partial differential equations, studies nonlinear partial differential equations of the so-called dispersive type, which are related to wave phenomena.
Examples include the KdV equation, a model of waves on shallow water such as canals, and the Schrödinger equation, the fundamental equation of quantum mechanics.
For nonlinear problems, a "solution formula" cannot be expected, so it is not even obvious whether an equation has a solution in the first place.
The professor is also interested in how solutions behave.
Key terms
- Dispersive type
- A group of nonlinear partial differential equations related to wave phenomena, including the KdV equation and the Schrödinger equation
- KdV equation
- An equation that serves as a model of waves on shallow water, such as in canals
- Schrödinger equation
- The fundamental equation of quantum mechanics
ResearchResearch themes
Differential equations are one kind of mathematical model used to explain phenomena. Associate Professor Tanaka studies dispersive nonlinear partial differential equations related to wave phenomena, and is interested in whether solutions exist and how they behave.
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MembersFaculty
- Associate ProfessorTomoyuki Tanaka
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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: “Soliton 2nd order” Alessio Damato / CC BY-SA 3.0 (cropped)
- Dispersive Nonlinear Partial Differential Equations: “Ripples dispersing sunlight into underwater rainbows in Brofjorden” W.carter / CC BY-SA 4.0 (cropped)
- Related lab (Analysis Lab (Erika Ushikoshi)): “Partial Differential Equations” Bernard Epstein / Public domain (cropped)
- Related lab (Algebra Lab): “Geometric sculpture at New Mersey Park” Rodhullandemu / CC BY-SA 4.0 (cropped)
- Related lab (Computational Fluid Dynamics Lab): “Catalytic-converter-simulation-velocity-streamlines” Atif Masood (FetchCFD) / CC BY-SA 4.0 (cropped)
- Related lab (Analytic Function Spaces and Operators Lab (Seiichiro Ueki)): “TetrationComplexColor” AJRobbins at English Wikipedia / Public domain (cropped)
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