6 papers
On the inverse scattering transform for the KdV equation with summable initial data
Alexei Rybkin
We consider the Cauchy problem for the Korteweg--de Vries equation with real initial data that is both and summable and supported on (0,\infty). Using the left refl…
Reconstruction of the non-linear wave at a buoy from shoreline data and applications to the tsunami inverse problem for piece-wise sloping bathymetry
Oleksandr Bobrovnikov, Madison Jones, Shriya Prasanna +3
We discuss the following inverse problem: given the run-up data of a tsunami wave, can we recover its initial shape? We study this problem within the framework of the non-linear sh…
A new asymptotic regime for the KdV equation with Wigner-von Neumann type initial data
Alexei Rybkin
We investigate the long-time asymptotic behavior of solutions to the Cauchy problem for the KdV equation, focusing on the evolution of the radiant wave associated with a Wigner-von…
The boundary control approach to the Titchmarsh-Weyl function
S. A. Avdonin, V. S. Mikhaylov, A. V. Rybkin
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the amplitude due to Simon and yields a new efficient method to ev…
Separation of the initial conditions in the inverse problem for 1D non-linear tsunami wave run-up theory
Alexei Rybkin, Oleksandr Bobrovnikov, Noah Palmer +2
We investigate the inverse tsunami wave problem within the framework of the 1D nonlinear shallow water equations (SWE). Specifically, we focus on determining the initial displaceme…
Inverse non-linear problem of the long wave run-up on coast
Alexei Rybkin, Efim Pelinovsky, Oleksandr Bobrovnikov +3
The study of the process of catastrophic tsunami-type waves on the coast makes it possible to determine the destructive force of waves on the coast. In hydrodynamics, the one-dimen…