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Applied Analysis Lab (Hironobu Sasaki)
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Tracing where the solutions of equations that describe waves are heading.
AboutAbout the lab
Finding unknown terms from scattering data
Prof. Sasaki studies solutions of nonlinear dispersive equations.
The subjects are equations that describe waves, such as the nonlinear Schrödinger equation and the Klein-Gordon equation.
The professor considers fundamental questions: how long a solution exists and which function it approaches.
The professor also works on an inverse problem: finding the unknown nonlinear term from observable scattering data.
Key terms
- Dispersive equation
- An equation describing waves whose speed of travel differs by wavelength. A wave packet gradually spreads out
- Scattering operator
- The correspondence linking an incoming wave to the wave that goes out far in the future
- Inverse problem
- The problem of finding the underlying mechanism from the results that can be observed
NewsLab news
View More ↗ResearchResearch themes
The professor studies solutions of nonlinear dispersive equations. They are important models in physics and engineering, and also stimulating objects of study in mathematics.
*Illustrative imageExistence of solutions and their asymptotic behavior
Does a solution exist for all time? If it does, which function does it approach? If it does not, when does it blow up? The professor considers these fundamental questions.
*Illustrative imageInverse scattering problem
This is the problem of finding the still-unknown nonlinear term from scattering data that are known through observation. It is pursued in parallel with the fundamental questions.
*Illustrative imageDetailed analysis of the scattering operator
The professor examines in detail how much of the smoothness and decay rate of solutions the scattering operator preserves. The difficulty of the problem changes depending on how the nonlinear term is chosen, and many parts remain unsolved.
MembersFaculty
- Associate ProfessorHironobu Sasaki
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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: “Water ripples” Georgios Orfeas Katsouris / CC BY 4.0 (cropped)
- Existence of solutions and their asymptotic behavior: “Wave packet (no dispersion) instance” User:Dicklyon / CC BY-SA 3.0 (cropped)
- Inverse scattering problem: “Diffraction-half-plane-no-rays” MikeRun / CC BY-SA 4.0 (cropped)
- Detailed analysis of the scattering operator: “Complex exponential function graph horn shape xvw dimensions” DCary / CC BY-SA 4.0 (cropped)
- Related lab (Applied Analysis Lab (Masaya Maeda)): “Soliton de Peregrine” Christophe.Finot / CC BY-SA 3.0 (cropped)
- Related lab (Applied Analysis Lab (Ishida)): “Dictyostelium Late Aggregation 2” Bruno in Columbus (talk) / Public domain (cropped)
- Related lab (Fundamental Analysis Lab (Kazuki Hiroe)): “Riemann sphere” Jean-Christophe BENOIST / CC BY-SA 3.0 (cropped)
- Related lab (Geometry (Sanda) Lab): “3D-Cylinder with handle and torus with hole” 作者不詳 / Public domain (cropped)
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