Nonlinear Wave Equations and Krein–de Branges theory

01.10.2020–30.09.2025
Research project
Principal investigator: Aleksey KOSTENKO (E101-01)

The main objects of our project are the most important 1+1 completely integrable nonlinear wave equations (the Korteweg-de Vries equation, the nonlinear Schrödinger equation, and the CamassaHolm equation) and the corresponding isospectral problems (1-D Schrödinger equation, 1-D Dirac equation, and strings, respectively). The inverse scattering transform (IST) approach is a very powerful tool to treat these equations. The IST approach enables us to construct explicit solutions and to perform a rather detailed analysis of initial value problems. However, it has a rather restrictive range of applicability. Indeed, the key ingredient is a solution of the corresponding inverse spectral/scattering problem and this immediately explains all the restrictions. Our major goal is to make a progress in understanding the inverse spectral/scattering theory of the above mentioned one-dimensional spectral problems.

Project team members: Prof. Harald WORACEK