Theoretical and Numerical Investigation of Nonlinear Mathematical Models

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Invited Lectures:

M.D. Todorov,
Generalized Wave Equations: Coupling, Polarization, Phase Difference, Quasi-Particle Dynamics of Localized Solutions.
University of Jonkoping, Dept of Mathematics, Physics & Chemistry, Sweden, March 4, 2015.

M.D. Todorov, V. Gerdjikov, A. Kyuldjiev,
Multisoliton Interactions for the Manakov System under Composite External Potentials.
Colloquium of Dept of Mathematics, College of Charleston, SC, March 30, 2015.

M.D. Todorov,
Soliton Dynamics and Interaction of Vector Schroedinger Equation.
School of Natural Sciences and Health, Tallinn University, 24 September 2015.

M.D. Todorov,
Soliton Dynamics of the Nonlinear Wave and Dispersive Equations. Boussinesq Paradigm.
Joint College of Arts & Sciences Research Seminar, Embrie-Riddle Aeronautical University, Daytona, FL, USA, July 11, 2016.

M.D. Todorov,
Localized Solutions of Generalized Wave Equations. Boussinesq Paradigm, Joint College of Arts & Sciences Research Seminar, Embrie-Riddle Aeronautical University, Daytona, FL, USA, April 5, 2017.

 

Conference Presentations:

Second stage of the project:

N. Kolkovska, M. Dimova, N. Kutev,
Stability of fast solitary waves in biomembranes and nerves, International Conference on Mathematical Methods and Models in Biosciences (BIOMATH 2016), June 19 - June 25, 2016, Bachinovo, Blagoevgrad, Bulgaria.

N. Papanicolaou,
A Discontinuous Galerkin Finite Element Method for High-Prandtl Number Non-Fourier Convection, 8th Conference "Application of Mathematics in Technical and Natural Sciences," Albena, June 22-27 2016.

M. Todorov,
Boussinesq Paradigm: Theory, Computer Simulation, Experiment, 6th All-Russian Conference with Foreign Participants "Free Boundary Problems: Theory, Experiment and Applications," Barnaul, Russia, August 7-11, 2017.

N. Papanicolaou,
Numerical Investigation of Biolm Growth in Microgravity, 9th Conference "Application of Mathematics in Technical and Natural Sciences," Albena, June 21-26 2017.

D. Georgieva,
Polarization Eects of Femtosecond Laser Pulses Due to Cubic Type Nonlinearity in Air, 26th Annual International Laser Physics Workshop, July 17-21, 2017, Kazan, Russia.

D. Georgieva,
Avalanche Parametric Conversion and White Light from Femtosecond Pulses in Glasses, 26th Annual International Laser Physics Workshop, July 17-21, 2017, Kazan, Russia.

D. Georgieva,
Femtosecond Limit of Soliton Propagation in Optical Fibers, July 17-21, 2017, Kazan, Russia.

N. Kolkovska, M. Dimova, N. Kutev,
Orbital stability or instability of solitary waves to Boussinesq paradigm equation with quadratic-cubic nonlinearity, 9th International Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17), June 21 - June 26, 2017, Albena, Bulgaria.

N. Kutev, N. Kolkovska, M. Dimova,
Global behavior of the solutions to ordinary differential equations and applications for nonlinear dispersive equations, Third International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES 2016), July 4 - July 9, 2016, Sofia, Bulgaria.

N. Kutev, M. Dimova, N. Kolkovska,
Necessary and sufficient condition for finite time blow up of the solutions to double dispersion equation, 9th International Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17), July 21 - June 26, 2017, Albena, Bulgaria.

N. Kutev, M. Dimova, N. Kolkovska,
Necessary and sufficient condition for finite time blow up of the solutions to Klein-Gordon equation, Fourth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES 2017), June 18 - June 22, 2017, Sofia, Bulgaria.

N. Kutev, M. Dimova, N. Kolkovska,
Necessary and sufficient conditions for finite time blow up of the solutions to Boussinesq equation, Second International Conference "Mathematics Days in Sofia"(MDS2017), July 10 - July 14, 2017, Sofia, Bulgaria.

M. Todorov,
Long-time Dynamics and Interaction of Ultrashort Light Pulses, Minisymposium "Nonlinear Waves and Integrability," Mathematical Days in Sofia, July 10-14, 2017.

D. Georgieva,
Mathematical Modelling of the Processes of Generation, Interaction and Reduction of Optical Filaments, Minisymposium "Mathematical Modelling and Scientific Computing," Mathematical Days in Sofia, July 10-14, 2017.

M. Dimova, N. Kolkovska, N. Kutev,
Theoretical and numerical studies of the finite time blow up to double dispersion equation, X International Conference on Structural Dynamics (EURODYN 2017), September 10 - September 13, 2017, Rome, Italy.

V.I. Vucheva, N.T. Kolkovska,
Numerical Investigation of Sixth Order Bousinesq Equation, 9th International Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17),June 21- June 26, 2017, Albena, Bulgaria.

V.I. Vucheva, N.T. Kolkovska,
Finite Difference Scheme of Sixth Order Bousinesq Equation, Second International Conference "Mathematics Days in Sofia July 10- July 17, 2017, Sofia, Bulgaria.

V.I. Vucheva, N.T. Kolkovska,
Energy Preserving Finite Difference Schemes for Sixth Order Boussinesq Equation, CMAPT Workshop Computational Mathematics and Approximation Theory, September 5- September 8,2017, Linz, Austria.

V.I. Vucheva, N.T. Kolkovska,
Convergence Analysis of Finite Difference Scheme for Sixth Order Boussinesq Equation, 15th International Conference of Numerical Analysis and Applied Mathematics, September 25- September 30, 2017, Thessaloniki, Greece.

N.T. Kolkovska, V.I. Vucheva
Energy Preserving Finite Difference Scheme for Sixth Order Boussinesq Equation, X International Conference on Structural Dynamics, 10.09.2017 - 13.09.2017, Rome, Italy.

N. Kutev, S. Tabakova, S. Radev,
Velocity and Shear Rate Estimates of Some Non- Newtonian Oscillatory Flows in Tubes, 8th International Conference of the Euro- American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16), June 22-June 27, 2016, Albena, Bulgaria.

I. Bazhlekov, E. Bazhlekova,
Fractional derivative model for diffusion-controlled adsorption at liquid/liquid interface, Second Int. Conf. Mathematics Days in Sofia, Sofia, Bulgaria, July 10-14, 2017.

I. Bazhlekov,
Generalization of Ward-Tordai equation for time-fractional diffusion, Int. Conf. Applications of Generalized Functions in Harmonic Analysis, Mechanics, Stochastics and PDE (AGF:HAMSaPDE), Novi Sad, Serbia, 25-27 October, 2017.

I. Hristov, R. Hristova, S. Dimova,
Hybrid MPI+OpenMP parallelization of a leapfrog algorithm for solving systems of 2D Sine-Gordon equations, Seminar in LIT, JINR, Dubna, Russia, May 26, 2016.

I. Hristov, R. Hristova, S. Dimova,
Parallelization of a Finite difference scheme for solving systems of 2D Sine-Gordon equations, 7th International Conference "Distributed Computing and Grid-technologies in Science and Education, 2016, Dubna, Russia.

I. Hristov, G. Goranov, R. Hristova,
Nonlinear wave simulation on the Xeon Phi Knights Landing Processor, International Conference "Mathematical Modeling and Computational Physics, 2017 (MMCP2017), Dubna, Russia.

S. Dimova, I. Hristov, R. Hristova,
Standing wave solutions in systems of 2D Sine-Gordon equations: a numerical study. Int. scientiffic conference "Contemporary Problems of Mathematical Physics and Computational Mathematics, dedicated to the 110 anniversary of academician A.N.Tikhonov. October 31 - November 3, 2016. Faculty of CMC, M.V. Lomonosov MSU, Moscow, Russia.

I. Hristov, S. Dimova, R. Hristova,
Numerical simulation of 2D Sine-Gordon waves. Second International Conference "Mathematics Days in Sofia" (MDS'2017), July 10-14, 2017, Sofia, Bulgaria.

S. Dimova,
Nonsymmetric and Nonstandard Galerkin Methods for Nonlinear Problems. Int. Conference "Computational Methods in Applied Mathematics (CMAM-7). 100 Years of Galerkin Method July 31 - August 6, 2016, University of Jyvaskyla, Finland.

A. Fabricant, N. Kutev, T. Rangelov,
Estimates from Below for the First Eigenvalue of the p-Laplacian, Second International Conference "Mathematics Days in Sofia"(MDS2017), July 10 - July 14, 2017, Sofia, Bulgaria.

I. Bazhlekov, E. Bazhlekova,
Numerical approaches to unidirectional viscoelastic flows with fractional derivative models, International Conference on Fractional Differentiation and its Applications, ICFDA 2016, Novi Sad, Serbia, 18-20 July, 2016.

E. Bazhlekova,
Fractional Jeffreys' fluids: thermodynamic constraints, Stokes' first problem and subordination, International Conference on Fractional Differentiation and its Applications, ICFDA 2016, Novi Sad, Serbia, 18-20 July, 2016.

E. Bazhlekova,
Poiseuille flow of fractional Jeffreys' fluid in a rectangular channel - Analytical results, 15th Int. Conf. of Numerical Analysis and Applied Mathematics (ICNAAM 2017), Thessaloniki, Greece, 25-30 September, 2017.

I.Bazhlekov,
Poiseuille flow of fractional Jeffreys' fluid in a rectangular channel - Numerical results, 15th Int. Conf. of Numerical Analysis and Applied Mathematics (ICNAAM 2017), Thessaloniki, Greece, 25-30 September, 2017.

E. Bazhlekova,
Stokes' first problem for fractional Maxwell fluids, Fourth Int. Conf. New Trends in the Applications of Differential Equations in Sciences, NTADES 2017, Sofia, Bulgaria, 18-22 June, 2017.

E. Bazhlekova, I. Bazhlekov,
Subordination approach to time-fractional diffusion-wave equation of distributed order, Second Int. Conf. Mathematics Days in Sofia, Sofia, Bulgaria, July 10-14, 2017.

E. Bazhlekova, I. Bazhlekov, I. Georgiev,
Subordination approach to fractional wave equations, 8th Int. Conf. Transform Methods and Special Functions TMSF 2017, Sofia, Bulgaria, 27-30 August 2017.

E. Bazhlekova,
Positivity of fundamental solutions of distributed-order timefractional wave equations, Int. Conf. Applications of Generalized Functions in Harmonic Analysis, Mechanics, Stochastics and PDE ( AGF:HAMSaPDE), Novi Sad, Serbia, 25-27 October, 2017.

B. Batgerel, S.N. Dimova, T.N. Kupenova, I.V. Puzynin, T.P. Puzynina, I.G. Hristov, R.D. Hristova, Z.K. Tukhliev, Z.A. Sharipov,
Modelling Thermal Effects in Metals Irradiated by Copper Nanoclasters. The International Conference "Mathematical Modeling and Computational Physics"(MMCP'2017), July 3-7, 2017, Dubna, Russia.

B. Batgerel, S. Dimova, I.V. Puzynin, T.P. Puzynina, Z.K. Tukhliev, I.G. Hristov, R.D. Hristova, Z.K. Tukhliev, Z.A. Sharipov,
Evolution of Continuously-Atomistic Approach for Modelling the Irradiation of Metals by Heavy Ions. The International Conference "Mathematical Modeling and Computational Physics"(MMCP'2017), July 3-7, 2017, Dubna, Russia.

I. Georgiev,
Blood Flow Simulations in CT Based Geometries, 11th International Conference "Large-Scale Scientiffic Computations June 5-9, 2017, Sozopol, Bulgaria.

I. Georgiev,
GPU simulations of blood flow in CT based domains, International Conference Mathematical Modeling and Computational Physics, July 3-7, 2017, Dubna, Russia

I. Georgiev, S. Zolotarev,
Parallel tomography reconstruction using SART and OpenGL, Summer School &Workshop "Quantitative Tomographic Imaging - Radon meets Bell and Maxwell July 10-14, 2017, Linz, Austria

M.D. Todorov,
System of Coupled Nonlinear Schrodinger Equations with Different Cross-Modulation Rates, The Tenth IMACS Intl Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, University of Georgia, Athens, GA, USA, March 29-April 1, 2017.

M.D. Todorov,
Long-Time Dynamics and Interaction of Ultrashort Light Pulses, SIAM Conference on Dynamical Systems, Snowbird, UT, USA, May 21-25, 2017.

M.D. Todorov,
Boussinesq Paradigm: Theory, Computer Simulation, Experiment, 6th All-Russian Conference with Foreign Participants "Free Boundary Problems: Theory, Experiment and Applications", Barnaul, Russia, August 7-11, 2017.

First stage of the project:

M.D. Todorov, V. S. Gerdjikov, A. Kyuldjiev,
On N-soliton Interactions of Gross-Pitaevsky Equation in Two Space-time Dimensions.
9th IMACS Conference on Nonlinear Waves: Computation and Theory, Athens, GA, USA, April 1-4, 2015.

V. S. Gerdjikov, M.D. Todorov, A.V. Kyuldjiev,
Modeling Manakov Soliton Trains: Effects of External Potentials and Inter-channel Interactions.
9th IMACS Conference on Nonlinear Waves: Computation and Theory, Athens, GA, USA, April 1-4, 2015.

E. Bazhlekova,
Completely Monotone Functions in the Study of a Class of Fractional Evolution Equations.
Conference "Pannonian Mathematical Modelling, Dedicated to the Memory of Professor Mirjana Stojanovic", Novi Sad, Serbia, April 25-26, 2015.

I. Bazhlekov, D. Vasileva,
Numerical Simulation of Drop Coalescence in the Presence of Soluble Surfactant.
Conference "Pannonian Mathematical Modelling, Dedicated to the Memory of Professor Mirjana Stojanovic", Novi Sad, Serbia, April 25-26, 2015.

D. Georgieva,
Nonlinear interaction between Rogue waves, XXth International Conference Nonlinear Evolution Equations and Dynamical Systems (NDEES'15), May 24-31, 2015, S. Margherita di Pula, Sardinia, Italy.

M. Dimova, N. Kolkovska, N. Kutev,
Nonexistence of Global Solutions to Generalized Boussinesq Equation with Arbitrary Energy.
International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM 2015), Istanbul, Turkey, June 3-6, 2015.

T. Chernogorova, I. Dimov, L. Vulkov,
A Splitting Numerical Method for Primary and Secondary Pollutant Models.
10th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, June 8-12, 2015.

T. Chernogorova, L. Vulkov,
A Numerical Approach to Price Path Dependent Asian Options.
10th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, June 8-12, 2015.

S. Radev, S. Tabakova, N. Kutev, Application of the Carreau viscosity model to the oscillatory flow in blood vessels, 41st International Conference "Applications of Mathematics in Engineering and Economics", June 8-13, 2015, Sozopol, Bulgaria

N. Kutev, N. Kolkovska, M. Dimova,
Stability and Instability of Improved Heimburg-Jackson Model to Nerve Pulse Propagation.
International Conference on Mathematical Methods and Models in Biosciences (BIOMATH), Blagoevgrad, Bulgaria, June 14-19, 2015.

E. Bazhlekova, I. Bazhlekov,
Peristaltic Transport of Viscoelastic Bio-fluids with Fractional Derivative Models.
International Conference on Mathematical Methods and Models in Biosciences (BIOMATH), Blagoevgrad, Bulgaria, June 14-19, 2015.

I. Bazhlekov, D. Vasileva, E. Bazhlekova,
Mathematical Modelling of the Effect of Biosurfactants on the Surface Tension.
International Conference on Mathematical Methods and Models in Biosciences (BIOMATH), Blagoevgrad, Bulgaria, June 14-19, 2015.

N.C. Papanicolaou, A.C. Aristotelous,
High-Order Discontinuous Galerkin Methods for Coupled Thermoconvective Flows under Gravity Modulation.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

M.A. Christou,
A Sixth Order Generalized Boussinesq Type Equation using Hirota’s Method.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

N. Kolkovska, Kr. Angelow,
Numerical computation of the critical energy constant for two-dimensional Boussinesq equations.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

N. Kutev, N. Kolkovska, M. Dimova,
Generalized Nehari Functional and Global Solvability of Boussinesq Equation.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

M.E. Todorova, M.D. Todorov, T.P. Todorov, I.G. Koprinkov,
Robust Ultrashort Laser Pulse Formation in Ionization Free Regime Propagation.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

V.S. Gerdjikov, A.V. Kyuldjiev, M.D. Todorov,
Manakov Soliton Trains and External Potentials: Criterium of Adiabaticity. Part I and Part II.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

D.A. Georgieva, L.M. Kovachev,
Merging and Energy Exchange between Optical Filaments.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

I. Bazhlekov, D. Vasileva,
Numerical Modeling of Biosurfactants in Multiphase Flows.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

S. Dimova, Ts. Bazlyankov,
Numerical methods for Hamiltonian Systems: Implementation and Comparison,
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

E. Bazhlekova, I. Bazhlekov,
On the Rayleigh-Stokes Problem for Generalized Oldroyd-B Fluids.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

D. Vasileva, I. Bazhlekov, E. Bazhlekova,
Finite-difference approximation for two-dimensional generalized time-fractional Oldroyd-B fluids.
7th Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015.

M.D. Todorov,
Collision Dynamics of Coupled Nonlinear Schrodinger Equations.
Second International Conference New Trends in the Applications of Differential Equations in Sciences - NTADES 2015, 6-10 July 2015, Sofia (Bulgaria).

N. Kutev, N. Kolkovska, M. Dimova,
Finite time blow up of the solutions to Klein-Gordon equation via revised concavity method.
Second International Conference New Trends in the Applications of Differential Equations in Sciences - NTADES 2015, 6-10 July 2015, Sofia (Bulgaria).

D. Vasileva, I. Bazhlekov, E. Bazhlekova,
A compact finite-difference scheme for two-dimensional fractional Oldroyd-B fluids.
Second International Conference New Trends in the Applications of Differential Equations in Sciences - NTADES 2015, 6-10 July 2015, Sofia (Bulgaria).

N. Kolkovska,
Numerical Evaluation of 2D Ground States.
Mathematical Modeling and Computational Physics 2015 , 13-17 July 2015, Stara Lesna, Slovakia.

S. Dimova,
WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems.
Mathematical Modeling and Computational Physics 2015 , 13-17 July 2015, Stara Lesna, Slovakia.

K. Angelow,
Asymptotic Behavior of the Stationary Wave Solutions to a Two Dimensional Boussinesq Equation Workshop on Approximation Theory, CAGD, Numerical Analysis and Symbolic Computation, August 24-29, 2015, Linz, Austria.

M.D. Todorov,
Collision Dynamics of Vector Schroedinger Equation.
Lavrentyev Readings on Mathematics, Mechanics and Physics, Novosibirsk, Russia, September 7-11, 2015.

M.D. Todorov,
Vector Schrodinger Equation: Coupling, Polarization, Phase Difference, Quasi-Particle Dynamics, National Conference Mathematical Modeling and Mathematical Physics devoted to the 165th anniversary of the Sofia Kovalevskaya birth, Kremenchuk, Ukraine, September 22-25, 2015.

S.N. Dimova,
Adaptive numerical procedures based on the invariant properties of the continuous models.
Advanced Mathematics, Computations and Applications, Novosibirsk, Russia, October 19-23, 2015.

E. Bazhlekova, I. Bazhlekov,
Fractional derivative models for unidirectional viscoelastic flows, Fractional Calculus and Applications 2015, Bulgarian-Serbian symposium, Sofia, Bulgaria, December 8, 2015.

M. Todorov,
Soliton Dynamics and Interaction of Vector Schroedinger Equation. Consistency and Integrability, December 9-11, 2015 Workshop Mathematical Modeling and Scientific Computing, Velingrad.

R. Hristova, I. Hristov,
Standing Waves in Systems of Perturbed Sine-Gordon Equations, 10th Annual Meeting of the Bulgarian Section of SIAM (BGSIAM'15), December 21-22, 2015, Sofia, Bulgaria

M. Christou, A. Polycarpou,
On-Axis Electromagnetic Scattering from a Sub-Wavelength Aperture on a Conducting Screen, poster session, 8th AMiTaNS Conference, Albena, Bulgaria, June 22-27, 2016.

M. Todorov,
Soliton Dynamics, Adiabaticity and Interaction of Vector Schroedinger Equation, 3rd International Conference on Structural Nonlinear Dynamics and Diagnosis, Marrakech (Morocco), May 23-25, 2016.

M. Todorov,
Numerical Investigation of the Dynamics of High-Intensity Ultrashort Light Pulses, special session "Nonlinear Waves: Coherent Structures and Complex Dynamics", 11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, USA, July 1-5, 2016.

M. Todorov,
Vector Schroedinger Equation: Quasi-Particle Concept of Evolution and Interaction of Solitary Waves, SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, PA, USA, August 9-11, 2016.

 

 

 

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