This is a brief survey article discussing simple yet very rich models for free surface flows over
topographical features. We consider the most interesting case where the flow is near critical …

Multiscale Atmosphere–Ocean Interactions and the Low-Frequency Variability in the
Equatorial Region in: Journal of the Atmospheric Sciences Volume 74 Issue 8 (2017) Jump …

We construct and discuss a linearization method for solving Burgers equation with time-
dependent coefficients and a nonlinear forcing term. Our results are shown to contain and …

We construct new types of arbitrary-order Darboux transformations for the stationary forced
Burgers equation in one dimension. The distinguishing property of these transformations is …

In this paper we study some key effects of a discontinuous forcing term in a fourth order
wave equation on a bounded domain, modeling the adhesion of an elastic beam with a …

In this paper a nonlinear observer for a class of partial differential equations known as the
advection equation is designed. The observer, that uses only boundary measurements, is …

Gathering together some existing results, we show that the solutions to the one-dimensional
Burgers equation converge for long times towards the stationary solutions to the steady …

The purpose of this thesis is to study energy transfer in nonlinear systems. In the first part, I
focus on a model of two nonlinearly coupled (complex) oscillators subject to stochastic …

In the present study a simplified multiscale atmosphere-ocean coupled model for the tropical
interactions among synoptic, intraseasonal and interannual scales is developed. Two …

The response to resonant and near-resonant forcing is studied in a simple model using the
forced inviscid Burgers equation ut+(u2 2) x= f. The nonlinear term represents …