Alexei Rybkin
1998 | Professor of Mathematics
Leningrad State University 1985, PhD
CH 304B | 907-474-6002
arybkin@alaska.edu
Broadly speaking, water is my business. More specifically, I study nonlinear partial
differential equations that model (among many other physical phenomena) water waves.
I maintain two large lines of research: theoretical and applied. In the theoretical
part I study completely integrable systems by inverse spectral and scattering methods
in connection with fluid mechanics. In the applied part I collaborate with geophysicists
on shallow water waves systems that are used in modeling tsunami waves. For this activity
I hire graduate and undergraduate students.
Highlighted work:
鈥淭he binary Darboux transformation revisited and KdV solitons on arbitrary short-range
backgrounds鈥, Studies in Applied Math (2021), to appear.
鈥淭he Generalized Carrier鈥揋reenspan Transform for the Shallow Water System with Arbitrary
Initial and Boundary Conditions鈥, Water Waves 1 (2021), vol 3, 268-295 (with D. Nicolsky,
E. Pelinovsky, and M. Buckle) *.
鈥淥n classical solutions of the KdV equation鈥, Proc. London Math. Soc. (3) 121 (2020)
354鈥371 (with S. Grudsky)
"General Initial Value Problem for the Nonlinear Shallow Water Equations: Runup of
Long Waves on Sloping Beaches and Bays", Physics Letters A 382 (2018) 2738鈥2743 (with
A. Raz, D. Nicolsky, and E. Pelinovsky) *.
鈥淣onlinear wave run-up in bays of arbitrary cross-section: generalization of Carrier-Greenspan
approach鈥, J. Fluid Mech. (2014), vol. 748, pp. 416-432 (with I. Didenkulova and E.
Pelinovsky).
*denotes contributing undergraduates in REU program