44 citations · 151 across the 23 of their papers we have counts for
24 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…
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…
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…
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…