Theoretical and Numerical Investigation of Nonlinear Mathematical Models

The project “Theoretical and Numerical Investigation of Nonlinear Mathematical Models” is funded under contract I02/9 from 12.12.2014 by the National Science Fund of the Bulgarian Ministry of Education and Science under the call Financing of Scientific Research in Priority Areas–2014.

The applicant organization is the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (IMI, BAS), partner organizations are the Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski” (FMI, SU), the Technical University of Sofia (TU) and the University of Nicosia, Cyprus (UN).

FMI, SU and IMI, BAS have had very fruitful scientific and educational cooperation during the years. They are closely connected in the frame of ECMI as well—the two Bulgarian Study Groups with Industry—ESGI’95 (2013) and ESGI’104 (2014), were hosted by IMI. The next one—ESGI’113 (September 14–18, 2015), together with the Preparatory student’s Modelling week (September 7–11, 2015)—will also be hosted by IMI. We believe that involving scientists from the four institutions will assure the success of such an interdisciplinary project.

The real processes in nature and society are essentially nonlinear. Due to the lack of general theory of the nonlinear mathematical models, their investigation is still a serious challenge to the researchers. The goal of the project is theoretical and numerical study of the mathematical models of important for technology and society nonlinear processes.

The research is organized into six work packages:

  • WP1. Investigation of the dynamics of solitary waves as solutions of nonlinear wave and amplitude equations.
  • WP2. Investigation of nonlinear dispersive equations that model the distribution of surface waves with/without surface tension and the dynamics of nonlinear lattices.
  • WP3. Investigation of the dynamics of drops in viscous flows.
  • WP4. Investigation of the dynamics of the processes in multilayer superconductors of Josephson type.
  • WP5. Theoretical and numerical analysis of financial and ecological mathematical models.
  • WP6. Theoretical and numerical study of non-Newtonian flows in heterogeneous porous media using fractional calculus.

The methods of investigation will be tailored to the peculiarities of the nonlinear mathematical models—nonuniqueness of their solutions, occurrence of singularities from smooth initial data, localization of the solutions in space and time (self-dispersing and blow up in finite time). Important characteristics of the real processes will be obtained through a rigorous study of the mathematical models and further recommendations for their optimization will be made. At the same time advanced efficient and reliable numerical methods and algorithms for solving the discrete problems will be developed and analyzed by using multiprocessor clusters and grid computing.

The research is in harmony with the National strategies 2014–2020.