October 26, 2023

Modelling of Tsunami Waves

How is the tsunami initiated? The thrust of a mathematical approach is to examine how a wave, once initiated, moves, evolves and eventually becomes such a destructive force of nature. We aim of this talk is to describe how an initial disturbance gives rise to a tsunami wave. We study the propagation of tsunamis from their small disturbance at the sea level to the size they reach approaching the coast. It is clear that in order to predict accurately the appearance of a tsunami it is fundamental to build up a good model. From this point of view the most important tool in the context of water waves is soliton theory. Frequently in the literature it is stated that a tsunami is produced by a large enough soliton. Solitons arise as special solutions of a widespread class of weakly nonlinear dispersive partial differential equations modelling water waves, such as the KdV or Camassa-Holm equation, representing to various degrees of accuracy approximations to the governing equations for water waves in the shallow water regime. 

Even with the aid of the most advanced computers it is not possible to find the exact solutions to the nonlinear governing equations for water waves. For this purpose we introduce the Cellular Nonlinear Network (CNN) approach to discretize the governing equation over a suitable grid. We develop algorithm for studying the tsunami waves based on CNN approximation.

About the speaker

Angela Slavova is a Bulgarian applied mathematician. She heads the Department of Mathematical Physics in the Institute of Mathematics of the Bulgarian Academy of Sciences, and is former chair of the Bulgarian section of the Society for Industrial and Applied Mathematics.

Slavova graduated from the University of Ruse with M.S. in computer engineering in 1986. From 1992 to 1993 she was a Fulbright scholar at the Florida Institute of Technology, but returned to Bulgaria to obtain her Ph.D. in mathematics in 1995 from her alma mater and in 2005 became Doctor of Science at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences.

From 2004 to 2011 Slavova was a head of the Department of Mathematical Physics of the Institute of Mathematics at the Bulgarian Academy of Sciences. Since 2007 she has been a full professor at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences. Since 2011 she is a head of the Department of Differential Equations and Mathematical Physics at the Institute of Mathematics, Bulgarian Academy of Sciences.  She chaired the Bulgarian section Society for Industrial and Applied Mathematics for 2013–2014.

Slavova is the author of the textbook Cellular neural networks: dynamics and modelling (Kluwer, 2003). With Petar Popivanov, she wrote Nonlinear waves: An introduction (World Scientific, 2011) and Nonlinear waves: A geometrical approach (World Scientific, 2019).