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:

 “The binary Darboux transformation revisited and KdV solitons on arbitrary short-range backgrounds”, Studies in Applied Math (2021), to appear.

 “The Generalized Carrier–Greenspan Transform for the Shallow Water System with Arbitrary Initial and Boundary Conditions”, Water Waves 1 (2021), vol 3, 268-295 (with D. Nicolsky, E. Pelinovsky, and M. Buckle) *. 

“On classical solutions of the KdV equation”, Proc. London Math. Soc. (3) 121 (2020) 354–371 (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) 2738–2743 (with A. Raz, D. Nicolsky, and E. Pelinovsky) *. 

“Nonlinear wave run-up in bays of arbitrary cross-section: generalization of Carrier-Greenspan approach”, J. Fluid Mech. (2014), vol. 748, pp. 416-432 (with I. Didenkulova and E. Pelinovsky).

*denotes contributing undergraduates in REU program