Publications

Theoretical and Numerical Investigation of Nonlinear Mathematical Models

Publications:

Second stage of the project:

A. Compelli, R. Ivanov, and M.D. Todorov, Hamiltonian Models for the Propagation of Irrotational Surface Gravity Waves over a Variable Bottom, Philosophical Transactions of the Royal Society A 376, doi: 10.1098/rsta.2017.0091 (see also arXiv:1708.06791 [physics.flu-dyn])

K. Georgiev, M.Todorov, I. Georgiev (Eds) Advanced Computing in Industrial Mathematics, Revised Selected Papers of the 11th Annual Meeting of Bulgarian Section of SIAM, December 20-22 2016, Sofia, Bulgaria (VIII, 227 pages, 19 peer reviewed articles), Studies in Computational Intelligence vol.728, Springer, Switzerland, ISBN 978-3-319-65529-1 ISSN 1860-949X, DOI: 10.1007/978-3-319-65529-1.

R.Carretero, V.S.Gerdjikov, and M.D.Todorov, N-Soliton Interacions: Effects of Linear and Nonlinear Gain and Loss, In M.D.Todorov (Ed.) 9th International Conference "Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17), 2017, Albena, Bulgaria, American Institute of Physics Conference Proceedings, vol.1895, paper 040001, 10p., doi:10.1063/1.5007368

K. Christou, M.A. Christou, 2D solitons in Boussinesq equation with dissipation, Computational and Applied Mathematics, doi:10.1007/ s40314-015-0239-y, 2015, IF=0.437

M.A. Christou, N.C. Papanicolaou and C. Sophocleous, Numerical Similarity Solution for a Variable Coefficient K(m; n) Equation, Computational and Applied Mathematics (COAM), 1-14, Springer, 2016, ISSN 1807-0302, (Imp.F=0.961)

A.C. Aristotelious and N.C. Papanicolaou A Discontinuous Galerkin Method for Unsteady Two-Dimensional Convective Flows, in 8th International Conference "Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16)," 2016, Albena, Bulgaria, American Institute of Physics Conference Proceedings, vol.1773, paper 110002, 12p., 2016, doi:10.1063/1.4965006, (SJR=0.152).

M.A. Christou, N.C. Papanicolaou, C. Sophocleous, and C.I. Christov (2017) The Christov-Galerkin Spectral Method in Complex Arithmetics, in 9th International Conference "Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17), 2017, Albena, Bulgaria, American Institute of Physics Conference Proceedings, vol.1895, paper 120003, 9p., doi:10.1063/1.5007420, (SJR=0.163)

M.A. Christou, Sixth Order Solitary Wave Equations, Wave Motion 71, 18-24, 2017, doi:10.1016/j.wavemoti.2016.05.011, (Imp.F.=1.575)

A.C. Aristotelious and N.C. Papanicolaou, A Numerical Study of Biofilm Growth in a Microgravity Environment, in 9th International Conference "Application of Mathematics in Technical and Natural Sciences (AMiTaNS'17)," 2017, Albena, Bulgaria, American Institute of Physics Conference Proceedings, vol.1895, 2017, paper 120001, 8p., doi:10.1063/1.5007418, (SJR=0.163)

V.S. Gerdjikov, M.D. Todorov, and A.V. Kyuldjiev, Adiabatic Interactions of Manakov Solitons - Effects of Cross-Modulation. Wave Motion, 71 (2017), 71-81, doi:10.1016/j.wavemoti.2016.08.004 (see also arXiv:1610.08413 [nlin.SI]) (IF=1.575)

I.C. Christov, M.D. Todorov, S. Yoshida (Guest Eds), Mathematical Modeling and Physical Dynamics of Solitary Waves: From Continuum Mechanics to Field Theory, Special issue of Wave Motion, DOI: 10.1016/j.wavemoti.2016.09.007, Wave Motion 71, June 2017, 12 papers, 138p, ISSN 0165-2125, IF=1.575

K. Georgiev, M.Todorov, I. Georgiev (Eds) Advanced Computing in Industrial Mathematics, Revised Selected Papers of the 10th Annual Meeting of Bulgarian Section of SIAM, December 21-22 2015, Sofia, Bulgaria (262 pages, 21 peer reviewed articles), Studies in Computational Intelligence vol.681, Springer, Switzerland, ISBN 978-3-319-49543-9, ISSN 1860-949X, DOI: 10.1007/978-3-319-49543-9.

N. Kutev, N. Kolkovska, M. Dimova, Necessary and sufficient condition for finite time blow up of the solutions to sixth order double dispersive equations, Pliska Stud. Math. 28 (2018), 45-56.

N. Kutev, N. Kolkovska, M. Dimova, Nonexistence of global solutions to new ordinary differential inequality and applications to nonlinear dispersive equations. Mathematical Methods in the Applied Sciences, 39(9) 2016, 2287-2297. DOI:10.1002/mma.3639 (IF:0.918)

N. Kolkovska, M. Dimova, N. Kutev, Stability or instability of solitary waves to double dispersion equation with quadratic-cubic nonlinearity. Mathematics and Computers in Simulation, 133(1) 2017, 249-264. doi:10.1016/j.matcom.2016.03.010 (IF=1.218)

N. Kolkovska, M. Dimova, N. Kutev, Nonstandard potential well method and application to sixth order Boussinesq equation with Bernoulli type nonlinearity, in M.D. Todorov (Ed.) 9th International Conference "Application of Mathematics in Technical and Natural Sciences" (AMiTaNS'17), 2017, Albena, Bulgaria , AIP Conf. Proc. 1895, Melville, New York, paper 050005, 10p., 2017, doi:10.1063/1.5007377, SJR=0.163

M.D.Todorov, (Ed) Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16), Proceedings of the 8th International Conference, Albena, Bulgaria, June 21-26, 2017, AIP Conf. Proc. 1895, Melville, New York, (668 pages, 73 peer reviewed articles), ISBN 978-0-7354-1579-9, ISSN 0094-243X

N.T. Kolkovska, V.I. Vucheva, Energy preserving finite difference scheme for sixth order Boussinesq equation, Procedia Engineering, Elsevier, 199, 1539-1543 (2017), doi.org/10.1016/j.proeng.2017.09.501, SJR=0.282

N.T. Kolkovska, V.I. Vucheva, Numerical investigation of sixth order Boussinesq equation, AIP Conference Proceedings, American Institute of Physics, 1895, (2017), DOI:doi: 10.1063/1.5007409, 110003-1-110003-8, SJR=0.163

N. Kutev, M. Dimova, N. Kolkovska, Global solvability to double dispersion equation with Bernoulli type nonlinearity via one parametric family of potential wells. Pliska Stud. Math., 26, 2016, 123-132.

S. Radev, S. Tabakova, N. Kutev, Asymptotic Study of the Nonlinear Velocity Problem for the Oscillatory Non-Newtonian Flow in a Straight Channel, in K. Georgiev et al. (eds.), Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence 728, (2018), 159-168, doi.org/10.1007/ 978-3-319-65530-7_15, SJR=0.246

I. Bazhlekov, D. Vasileva, Numerical modeling of drop coalescence in the presence of soluble surfactants, Journal of Computational and Applied Mathematics 293 (2016), 7-19, IF=1.266

I. Hristov, R. Hristova, S. Dimova, Parallelization of a finite difference scheme for solving systems of 2D Sine-Gordon equations, Selected Papers of the 7th International Conference Distributed Computing and Grid-technologies in Science and Education, 2016, pp.250-255.

R. Hristova, I. Hristov, Standing Waves in Systems of Perturbed Sine-Gordon Equations, Studies in Computational Intelligence, Advanced Computing in Industrial Mathematics, Springer, 2017, pp.53-59.

T. Chernogorova, I. Dimov, L. Vulkov, Coordinate Transformation Approach for Numerical Solution of Environmental Problems, In: Batkai A., Csomos P., Farago I., Horanyi A., Szepszo G. (eds) Mathematical Problems in Meteorological Modelling, Mathematics in Industry, vol. 24, pp. 117-127, 2017, Springer, Cham.

T. Chernogorova, Koleva, M.N., Valkov, R.L., A two-grid penalty method for American options, Comp. Appl. Math. (2017). doi:10.1007/s40314-017-0457-6, IF= 0.961

A. Fabricant, N. Kutev, T. Rangelov, Sharp Hardy inequalities in star- shaped domains with double singular kernels, Mediterr. J. Math. 14:21 (2017) https://doi.org/10.1007/s00009-016-0831-4, IF=0.868

E. Bazhlekova, I. Bazhlekov, Unidirectional flows of fractional Jeffreys' fluids: thermodynamic constraints and subordination. Computers and Mathematics with Applications 73(6), (2017), 1363-1376, doi.org/10.1016/j.camwa.2016.12.009, IF=1.531

E. Bazhlekova, I. Bazhlekov, Stokes' first problem for viscoelastic fluids with a fractional Maxwell model, Fractal and Fractional, 1(1), (2017), 7; doi:10.3390/ fractalfract1010007

E. Bazhlekova, I. Bazhlekov, Application of Dimovski's convolutional calculus to distributed-order time-fractional diffusion equation on a bounded domain, Journal of Inequalities and Special Functions, 8 (2017), 68-83.

E. Bazhlekova, I. Bazhlekov, Subordination approach to multi-term timefractional diffusion-wave equations, Journal of Computational and Applied Mathematics, (2017), in press, doi.org/10.1016/j.cam.2017.11.003, IF= 1.357

M.D.Todorov, (Ed) Application of Mathematics in Technical and Natural Sciences (AMiTaNS'16), Proceedings of the 8th International Conference, Albena, Bulgaria, June 22-27, 2016, AIP Conf. Proc. 1773, Melville, New York, (630 pages, 69 peer reviewed articles), ISBN 978-0-7354-1431-0, ISSN 0094-243X

N. Kutev, S. Tabakova, S. Radev, Velocity and shear rate estimates of some non-Newtonian oscillatory flows in tubes, in M.D.Todorov (Ed.) 8th International Conference "Application of Mathematics in Technical and Natural Sciences" (AMiTaNS'16), 2016, Albena, Bulgaria, AIP Conf. Proc. 1773, Melville, New York, paper 080002, 9p., 2016 (SJR>0.2), doi:10.1063/1.4964986

A. C. Aristotelous, N.C. Papanicolaou, A discontinuous Galerkin method for unsteady two-dimensional convective flows, in M.D.Todorov (Ed.) 8th International Conference "Application of Mathematics in Technical and Natural Sciences" (AMiTaNS'16), 2016, Albena, Bulgaria, AIP Conf. Proc. 1773, Melville, New York, paper 110001, 12p., 2016 (SJR>0.2), doi:10.1063/1.4965006

M.A. Christou, N.C. Papanicolaou, C. Sophocleous, Numerical similarity solution for a variable coefficient K(m,n) equation, Computational and Applied Mathematics (Springer), 2016, doi:10.1007/s40314-016-0387-8 (IF=0.802)

V.S. Gerdjikov, M.D. Todorov, A.V. Kyuldjiev, Adiabatic interactions of Manakov solitons - Effects of cross-modulation, Wave Motion (Elsevier), 2016, doi: 10.1016/j.wavemoti.2016.08.004 (IF=1.449)

E. Bazhlekova, I. Bazhlekov, Peristaltic transport of viscoelastic bio-fluids with fractional derivative models. Biomath, 5(1) 2016, DOI:10.11145/j.biomath.2016.05.161

E. Bazhlekova, K. Tsocheva, Fractional Burgers' model: thermodynamic constraints and completely monotonic relaxation function. C. R. Acad. Bulg. Sci., 69(7) 2016, 825-834. (IF:0.233)

Ang. Liolios, A. Moropoulou, Ast. Liolios, Kr. Georgiev, I. Georgiev, A Computational Approach for the Seismic Sequences Induced Response of Cultural Heritage Structures Upgraded by Ties, Studies in Computational Intelligence, 648 (2016), 47-58, SJR=0.246

D. Georgieva, L. Kovachev, and N. Nedyalkov, Avalanche Parametric Conversion in the Initial Moment of Filamentation, in Proc. SPIE, 10226, 102261G- 1, 2017, SJR = 0.228

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. European Physics Journal - Web of Conferences (EPJ-WoC), Proceedings of the International Conference 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. The development of Continuously-Atomistic Approach for Modelling the Irradiation of Metals by Heavy Ions. European Physics Journal - Web of Conferences (EPJ-WoC), Proceedings of the International Conference MMCP'2017, July 3-7, 2017, Dubna, Russia

A. Liolios, K. Liolios, A. Moropoulou, K. Georgiev, I. Georgiev, Cultural Heritage RC Structures Environmentally Degradated: Optimal Seismic Upgrading by Tention- Ties under Shear Effects, Lecture Notes in Computer Sciences, 10665 (2018), accepted, SJR=0.315

S. Zolotarev, V. Vengrinovich, M. Mirzavand, M. Mukhtar, I. Georgiev, Bayesian reconstruction of images of objects with high-density inclusions with suppression of artifacts, MATEC Web Conf., (2018), accepted, SJR=0.13

First stage of the project:

D.Shopova, M.D.Todorov, Phenomenological Description of Anisotropy Effects in Some Ferromagnetic Superconductors,
Physics Letters A 379 (2015), 1391-1396 (IF 1.683) (see also arXiv:1411.1748 [cond-mat.supr-con]).

V.S. Gerdjikov, M.D.Todorov, A.V. Kyuldjiev, Asymptotic behavior of Manakov solitons: Effects of potential wells and humps,
Mathematics and Computers in Simulation 121, (2016) 166-178, (IF=1.072) (see also arXiv:1408.0230v2[math-ph])

M.D.Todorov, V.S. Gerdjikov, A.V. Kyuldjiev, Multisoliton interactions for the Manakov system under composite external potentials, Proceedings of the Estonian Academy of Sciences 64, 3S, (2015) 368-378, doi:10.3176/proc.2015.3S.07, (IF=0.373)

V.S. Gerdjikov, A.V. Kyuldjiev, M.D.Todorov, Manakov solitons and effects of external potential wells, Discrete and Continuous Dynamical Systems. Supplement 2015, 505-514, doi:10.3934/proc.2015.0505 (SJR=1.131)

M.E. Todorova, M.D.Todorov, T.P. Todorov, I.G. Koprinkov, Robust ultrashort laser pulse formation in ionization-free regime propagation, in M.D.Todorov (Ed.) 7th International Conference "Application of Mathematics in Technical and Natural Sciences" (AMiTaNS'15), 2015, Albena, Bulgaria, AIP Conf. Proc. 1684, Melville, New York, paper 080012, 7p., 2015 (SJR=0.152), doi:10.1063/1.4934323

M.D.Todorov, (Ed) Application of Mathematics in Technical and Natural Sciences (AMiTaNS'15), Proceedings of the 7th International Conference, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, Melville, New York, (618 pages), ISBN 978-0-7354-1331-3, ISSN 0094-243X

D.A. Georgieva, L.M. Kovachev, Energy transfer between two filaments and degenerate four-photon parametric processes, Laser Phys. 25, 035402 (2015), doi: 10.1088/1054-660X/25/3/035402, (IF=1.025)

L.M. Kovachev, D.A. Georgieva, A.M. Dakova, Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments, Laser Phys. 25, 105402 (2015), doi:10.1088/1054-660X/25/10/105402, (IF=1.025)

K. Christou, M.A. Christou, 2D solitons in Boussinesq equation with dissipation, Computational and Applied Mathematics, doi:10.1007/s40314-015-0239-y, (2015), (IF=0.437)

N. Kutev, N. Kolkovska, M. Dimova, Finite time blow up of the solutions to Boussinesq equation with linear restoring force and arbitrary positive energy, Acta Mathematica Scientia, 36(3), (2016) 881-890. DOI:10.1016/S0252-9602(16)30047-9 (IF=0.742)

N. Kutev, M. Dimova, N. Kolkovska, Application of the improved concavity method to sixth order Boussinesq equations with arbitrary high initial energy, Pliska Stud. Math. 25 (2015), 91-104.

M. Dimova, N. Kolkovska, N. Kutev, Revised concavity method and application to Klein-Gordon equation, FILOMAT, 30(3) 2016, 831-839. DOI:10.2298/FIL1603831D (IF=0.638)

S. Tabakova, N. Kutev, S. Radev, Application of the Carreau viscosity model to the oscillatory flow in blood vessels, in AIP Conf. Proc. 1690, Melville, New York, paper 040019, 7p., 2015, doi:10.1063/1.4936726, SJR=0.152

N. Kutev, S.Tabakova, S. Radev, Approximation of the oscillatory blood flow using the Carreau viscosity model, in Ed. A.A. Tikhonov (Ed.) Proc. of the Int. Conference on Mechanics- Seventh Polyakhov's Reading, Russia, St. Petersburg, doi:10.1109/ POLYAKHOV.2015.7106747, IEEE, ISBN 978-1-4799-6824-4, IEEE Catalog number CFP15A24-ART, SJR=1.908

N. Kutev, N. Kolkovska, M. Dimova, Finite time blow up of the solutions to nonlinear Klein-Gordon equation with arbitrary high positive initial energy, Serdica Math. J. 41 (4) (2015), 481-492.

I. Hristov, R. Hristova, S. Dimova, Cavity and background oscillations in intrinsic Josephson junctions, arXiv:1511.02822, 2015

T. Chernogorova, I. Dimov, L. Vulkov, Coordinate transformation approach for numerical solution of environmental problems, in A. Batkai et al (Eds.), Springer special issue "Mathematical Problems in Meteorological Modelling", accepted

T. Chernogorova, L. Vulkov, A numerical approach to price path dependent Asian option, Lecture Notes in Computer Science 9374, (2015), 63-71, doi:10. 1007/978-3-319-26520-9_6, SJR=0.339

S. Dimova, Y. Mihaylova, Adaptive WENO schemes for singular in space and time solutions of nonlinear degenerate reaction-diffusion problems, EPJ Web of Conferences 108, 2016, accepted

K. Danov, S. Dimova, T. Ivanov, J. Novev, Shape analysis of a rotating axisymmetric drop in gravitational field: Comparison of numerical schemes for realtime data processing, Colloids and Surfaces A: Physicochemical and Engineering Aspects 489 (2016), 75-85, IF=2.752

I. Bazhlekov, D. Vasileva, Numerical modeling of drop coalescence in the presence of soluble surfactants,
Journal of Computational and Applied Mathematics 293 (2016), 7-19 (IF 1.266).

E. Bazhlekova, Completely monotone functions and some classes of fractional evolution equations ,
Integral Transforms and Special Functions 26 (2015), 737-752 (IF 0.723) (see also arXiv:1502.04647 [math.AP]).

N. Kutev, N. Kolkovska, M. Dimova, Sign-preserving functionals and blow-up to Klein–Gordon equation with arbitrary high energy,
Applicable Analysis 95(4) 2016, 860-873. DOI:10.1080/00036811.2015.1038994 (IF:0.803)

E. Bazhlekova, Subordination Principle for a Class of Fractional Order Differential Equations ,
Mathematics 3(2), 2015, 412-427.

N. Kutev, N. Kolkovska, M. Dimova, Revised concavity method and applications to nonlinear dispersive equations,
Scientific Reports of the Institute of Mathematics and Informatics - Bulgarian Academy of Sciences, 2/2015, ISSN 1314-541X.

T. Chernogorova, I. Dimov, L. Vulkov, A Splitting Numerical Method for Primary and Secondary Pollutant Models,
Lecture Notes in Computer Science 9374 (2015), 319-326 (SJR 0.339).

T. Chernogorova, L. Vulkov, On the Numerical Modeling of Pollution in Air, Water and Soil,
Proc. of the Fifth International Conference Research People and Actual Tasks on Multidisciplinary Sciences, 24–28 June 2015, Lozenec, Bulgaria, Publisher: Bulgarian National Multidisciplinary Scientific Network of the Professional Society for Research work, vol. 2, pp.117-121.

Ang. Liolios, A. Karabinis, Ast. Liolios, St. Radev, K. Georgiev, I. Georgiev, A computational approach for the seismic damage response under multiple earthquakes excitations of adjacent RC structures strengthened by ties,
Computers and Mathematics with Applications 70 (11) 2015, 2742-2751 (IF 1.697).

E. Bazhlekova, I. Bazhlekov, On the Rayleigh-Stokes problem for generalized fractional Oldroyd-B fluids,
AIP Conference Proceedings 1684, 080001, 2015 (SJR 0.152).

M.A. Christou, A.C. Polycarpou, Closed-form near-field expressions for electromagnetic scattering by an electrically small circular aperture on a conducting screen, AIP Conference Proceedings 1684, 080003, 2015 (SJR 0.152).

D.A. Georgieva, L.M. Kovachev, Merging and energy exchange between optical filaments, AIP Conference Proceedings 1684, 080005, 2015 (SJR 0.152).

V.S. Gerdjikov, M.D. Todorov, A.V. Kyuldjiev, Polarization effects in modeling soliton interactions of the Manakov model, AIP Conference Proceedings 1684, 080006, 2015 (SJR 0.152).

N. Kolkovska, K. Angelow, Numerical computation of the critical energy constant for two-dimensional Boussinesq equations, AIP Conference Proceedings 1684, 080007, 2015 (SJR 0.152).

N. Kolkovska, M. Dimova, N. Kutev, Generalized Nehari functionals and finite time blow up of the solutions to Boussinesq equation, AIP Conference Proceedings 1684, 080008, 2015 (SJR 0.152).

D. Vasileva, I. Bazhlekov, E. Bazhlekova, Alternating direction implicit schemes for two-dimensional generalized fractional Oldroyd-B fluids, AIP Conference Proceedings 1684, 0800014, 2015 (SJR 0.152).

S. Dimova, Ts. Bazlyankov, Numerical methods for Hamiltonian systems: Implementation and comparison, AIP Conference Proceedings 1684, 090002, 2015 (SJR 0.152).

N.C. Papanicolaou, A.C. Aristotelous, High-order discontinuous Galerkin methods for coupled thermoconvective flows under gravity modulation, AIP Conference Proceedings 1684, 090010, 2015 (SJR 0.152).

N. Kolkovska, Numerical Evaluation of 2D Ground States, to appear in EPJ Web of Conferences Journal, 2015.

D. Vasileva, I. Bazhlekov, E. Ayryan, E. Bazhlekova, A compact alternating direction implicit scheme for two-dimensional fractional Oldroyd-B fluids, Pliska Studia Mathematica Bulgarica 25 (2015), 213-224.

A. Fabricant, N. Kutev, T. Rangelov, Improved Hardy inequality and applications, Pliska Stud. Math. 25 (2015), 67-80

A. Fabricant, N. Kutev, T. Rangelov, Lower estimate of the first eigenvalue of p-Laplacian via Hardy inequality, C. R. Acad. Bulg. Sci. 68(5), (2015), 561-568, IF=0.214