On Ostrovsky-type models #

Karima Khusnutdinova, Matthew Tranter

11:50 Monday in 2Q42.

Part of the Advances in water waves and free-surface flows session.

Abstract #

Single and coupled Ostrovsky-type equations have been derived as reduced mathematical models describing nonlinear internal waves in a rotating ocean, as well as strain waves in bi-layers with an imperfect interface. I will discuss how one can by-pass the so-called “zero-mass” or “zero-mean” contradiction associated with the equations in the class of periodic functions on a finite interval for several cases of increasing complexity, and will discuss the typical dynamical behaviours described by the models [1,2].

References: [1] K.R. Khusnutdinova, M.R. Tranter, D’Alembert-type solution of the Cauchy problem for the Boussinesq-Klein-Gordon equation, Stud. Appl. Math. 142 (2019) 551-585. [2] K.R. Khusnutdinova, M.R. Tranter, Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction, Chaos 32 (2022) 113132.