Dynamics of Partial Differential Equations

Volume 17 (2020)

Number 2

Exact and explicit internal water waves at arbitrary latitude with underlying currents

Pages: 117 – 127

DOI: https://dx.doi.org/10.4310/DPDE.2020.v17.n2.a2


Yanjuan Yang (School of Mathematics and Statistics, Shandong Normal University, Ji’nan, China)

Xun Wang (Department of Mathematics, Shanghai Normal University, Shanghai, China)


We present an explicit exact solution to the nonlinear governing equations in the $\beta$-plane approximation for internal geophysical water waves propagating at an arbitrary latitude. Such a solution describes oceanic waves in the presence of a constant underlying current, which propagate eastward above the thermocline and beneath the near-surface layer where wind effects are confined.


exact and explicit solutions, internal geophysical waves, arbitrary latitude

2010 Mathematics Subject Classification

74G05, 76B15, 86A05

Received 8 August 2019

Published 24 February 2020