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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…