Sergey A Dyachenko
Department of Mathematics
University of Illinois at Urbana-Champaign.

Research:
Curriculum Vitae: My CV
Sergey Dyachenko on ResearchGate
Research Interests: My interest lies in fluid dynamics, specifically in the singularity formation in flows with
free surface. Dynamics of the ocean surface in the high steepness regime often demonstrates
breaking waves, and whitecapping at the crests of the steep waves. These spectacular events
are associated with singularity formation, and its evolution in the Euler (or Navier-Stokes)
equations with the free boundary.

In small steepness regime the envelope of a train of periodic travelling waves on the ocean surface
is described by the nonlinear Schroedinger equation (NLSE), which is a spectacularly rich and interesting
equation. The NLSE and other integrable systems are in the list of my most favoured models to work with.

My toolbox consists of computational mathematics and methods of applied mathematics. I enjoy coding in C,
Python, Matlab and Julia.
Research Interests (short version): Water waves (Link to Stokes wave website)
Nonlinear waves in optical media
Keller-Segel model
Bose-Einstein condensaion
Numerical simulations
Publications: 14. S. A. Dyachenko and Vera Mikyoung Hur,
    Stokes Waves with Vorticity II: Folds and Gaps , in preparation (2018)
13. A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov,
   Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion,
submitted to JFM (2018), arXiv link
12. S. A. Dyachenko,
   On the dynamics of a free surface of an ideal fluid in a bounded domain in the presence of surface tension,
J. Fluid Mech (2019), vol. 860, pp. 408-418 PDF
11. S. A. Dyachenko and Vera Mikyoung Hur,
    Stokes Waves with Vorticity I: Numerical Computation.,
Accepted to SAPM(2018) arXiv link
10. P. M. Lushnikov, S. A. Dyachenko, D. A. Silantyev,
   New Conformal Maping for Adaptive Resolving of the Complex Singularities of Stokes Wave,
Proc. Roy. Soc. A (2017), Link to paper
9. S. Dyachenko, A. Zlotnik, A., Korotkevich, M. Chertkov,
   Operator Splitting Method for Dynamic Simulations of Flows in Natural Gas Transport Networks , Physica D (2017)
8. S.A. Dyachenko, D.V. Zakharov, V.E. Zakharov,
   Primitive potentials and bounded solutions of the KdV equation , Physica D (2016)
7. D.V. Zakharov, S.A. Dyachenko, V.E. Zakharov,
   Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics , Lett. Math. Phys. (2016)
6. D.V. Zakharov, V.E. Zakharov, S.A. Dyachenko,
    Non-periodic one-dimensional ideal conductors and integrable turbulence , Physics Letters A (2016)
5. S.A. Dyachenko, A.C. Newell,
   Whitecapping , Stud. in Appl. Math (2016)
4. S.A. Dyachenko, P.M. Lushnikov, A.O. Korotkevich,
   Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pade approximation,, Stud. in Appl. Math (2016)
3. S.A. Dyachenko, P.M. Lushnikov, A.O. Korotkevich,
   Complex Singularity of a Stokes wave,, JETP Letters (2013)
2. P.M. Lushnikov, S.A. Dyachenko and N. Vladimirova
   Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,, Phys Rev A (2013)
1. S.A. Dyachenko, P.M. Lushnikov and N. Vladimirova
   Logarithmic scaling of the collapse in the critical Keller-Segel equation, Nonlinearity (2013)

Teaching:
Spring 2019: Intro to PDE
Fall 2018: Intro to PDE
Spring 2018: Applied Linear Algebra
Fall 2017: Differential Equations
Spring 2016: Intro to PDE
Fall 2015: Intro to Differential Equations Plus
Spring 2015: Linear Algebra (U of A)

Education
Ph.D.: University of New Mexico
Graduation: 18 August 2014
Academic Advisors: Prof. Pavel M. Lushnikov and Prof. Alexander O. Korotkevich
Topic: Strongly nonlinear phenomena and singularities in optical, hydrodynamic and biological systems
Higher education: University of New Mexico,
Albuquerque, USA,
MA: December 2010

Dissertation (PDF).
Moscow Institute of Physics and Technology,
Dolgoprudny, Moscow region,
BS: June 2007

Contacts
Office: Illini Hall 247A
E-mail: sdyachen@math.uiuc.edu
Address: Sergey A. Dyachenko
Department of Mathematics at UIUC,
1409 W. Green St,
Urbana, IL 61801 USA