Matlab codes:

  • BabenkoCG.m: his function computes the steady irrotational surface solitary (classical and generalized) capillary-gravity wave solutions of the full Euler equations (homogeneous, incompressible and perfect fluids). The full Euler system is recasted under the form of the Babenko equation using the conformal mapping technique. The wave is defined by its initial Froude and Bond numbers (Fr, Bo) and the result is about twelve digits accurate. The method works for all but the highest waves.

  • run_Euler.m: Fourier-type pseudo-spectral solver of the full Euler equations with the free surface on a fluid layer of infinite depth. The time-dependent fluid domain is transformed into a strip using the conformal mapping technique. Time discretization is done using the embedded Cash-Karp method of the order 5(4). The time integration is improved using the integrating factor technique (i.e. exact integration of linear terms). The solver is initialized to simulate the celebrated Peregrine breather evolution in the full Euler.

FreeFem++ codes:

In this section you will find useful pieces of codes and some other information:

  • biblio.bib: my BibTeX file containing 1400+ bibliographical items that I use in my publications. JabRef helps me a lot to manage this database.
  • All my presentations are prepared using Beamer package in LaTeX. The corresponding styles that I use can be downloaded here: beamerthemeKiev.sty and beamerthemeDnepropetrovsk.sty. To use theme, just put the command "\usetheme{Dnepropetrovsk}" or"\usetheme{Kiev}" in the beginning of your Beamer document.

My name is Denys Dutykh and I am an applied mathematician. On this site you will find some material related to my professional research activities. Some additional information is available here:


I am employed as a CNRS researcher at the Laboratory of Mathematics (LAMA UMR #5127), University of Savoie, France. My position is officially entitled "Chargé de Recherche CNRS", PhD, HDR.

My current research interests focus on the mathematical modeling of various natural processes. More specifically, we are interested in some phenomena arising in the fluid mechanics and water wave theory. Moreover, we develop efficient simulation tools and numerical methods to solve mathematical models under consideration.

I am completely open to new collaborations. Please, do not hesitate to contact me if you have any questions in the areas of my expertise and/or scientific interests. Any research and professional opportunities are welcome.