Publications

Numerical and Analytical Tools for Localized Solutions of Generalized Wave Equations in Multidimension

Publications:

N. Kolkovska: Two Families of Finite Difference Schemes for Multidimensional Boussinesq Paradigm Equation.
AIP Conference Proceedings, 1301 (2010), 395-403, SJR 0.142.

N. Kolkovska: Convergence of Finite Difference Schemes for a Multidimensional Boussinesq Equation.
Lecture Notes in Computer Science, 6046 (2011), 469-476, SJR 0.339.

C.I. Christov, N. Kolkovska, D. Vasileva: On the Numerical Simulation of Unsteady Solutions for the 2D Boussinesq Paradigm Equation.
Lecture Notes in Computer Science, 6046 (2011), 386-394, SJR 0.339.

C.I. Christov, N. Kolkovska, D. Vasileva: Numerical Investigation of Unsteady Solutions for the 2D Boussinesq Paradigm Equation.
Proc. BGSIAM’10 (5th Annual Meeting of the Bulgarian section of SIAM, 2010, Sofia), 2011, 11-16.

N. Kutev, N. Kolkovska, M. Dimova, C.I. Christov: Theoretical and numerical aspects for global existence and blow up for the solutions to Boussinesq paradigm equation.
AIP Conference Proceedings, 1404 (2011), 68-76, SJR 0.140.

C.I. Christov, M.D. Todorov, M.A. Christou: Perturbation solution for the 2D shallow-water waves.
AIP Conference Proceedings, 1404 (2011), 49-56, SJR 0.140.

N. Kolkovska, M. Dimova: A new conservative finite difference scheme for Boussinesq paradigm equation.
Central European Journal of Mathematics, 10 (2012), 1159-1171, IF 0.581.

M. Dimova, N. Kolkovska: Comparison of some finite difference schemes for boussinesq paradigm equation.
Lecture Notes in Computer Science, 7125 (2012), 215-220, SJR 0.332.

D. Vasileva, C.I. Christov: On the Numerical Investigation of Unsteady Solutions for the 2D Boussinesq Paradigm Equation in a Moving Frame Coordinate System.
Proc. BGSIAM’11 (6th Annual Meeting of the Bulgarian section of SIAM, 2011, Sofia), Demetra, Sofia, 2012, 103-108.

M. Todorov,C.I. Christov: Numerical Implementation of Fourier-transform Method for Generalized Wave Equations.
Proc. BGSIAM’11 (6th Annual Meeting of the Bulgarian section of SIAM, 2011, Sofia), Demetra, Sofia, 2012, 97-102.

N. Kutev, N. Kolkovska, M. Dimova: Global existence of Cauchy problem of Boussinesq paradigm equation,
Computers and Mathematics with Applications , 65 (2013), 500–511, IF 1.472.

N. Kolkovska, K. Angelow: A Multicomponent Alternating Direction Method for Numerical Solving of Boussinesq Paradigm Equation,
Lecture Notes in Computer Science, 8236 (2013), 371-378, SJR 0.332.

M. Dimova, D. Vasileva: Comparison of two numerical approaches to Boussinesq paradigm equation,
Lecture Notes in Computer Science, 8236 (2013), 255-262, SJR 0.332.

M. Christou: Soliton interactions on a Boussinesq type equation with a linear restoring force,
AIP Conference Proceedings 1404, Melville, NY, 41-48, SJR 161.

C.I. Christov: On the pseudolocalized solutions in multi-dimension of Boussinesq equation,
Mathematics and Computers in Simulation, IF 0.946, available online 4 Aug 2012, ( arXiv: 1202.4524v1, 21 Feb 2012).

M.D. Todorov: The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled systems of nonlinear Schroedinger equations,
Mathematics and Computers in Simulation, Available online 18 July 2014, (see also arXiv: 1202.5498v1, 21 Feb 2012).

C.I. Christov: Pseudolocalized three-dimensional solitary waves as quasi-particles,
arXiv: 1203.3779v1 [nlin.PS] 16 Mar 2012 (Opus Magnum).

D.A. Georgieva, L.M. Kovachev: Analytical solutions of the linear wave equation with finite energy,
AIP Conf. Proc., 1487 (2012), 264-271, SJR 0.161.

N.C.Papanicolaou, M.A.Christou, A.C.Polycarpou: Numerical Analysis of Nonlinear Electromagnetic Waves in Nematic Liquid Cristal Cells,
AIP Conf. Proc., 1487 (2012), 288-295, SJR 0.161.

L.M. Kovachev, D.A. Georgieva: A class of localized solutions of the linear and nonlinear wave equations,
Journal of Geometry and Symmetry in Physics, 27 (2012), 67-82, SJR 0.438.

V.S. Gerdjikov, M.D. Todorov: N-soliton Interactions for the Manakov System: Effects of External Potentials,
Localized Excitations in Nonlinear Complex Systems, Nonlinear Systems and Complexity 7, Springer International Publishing Switzerland 2014, 147-169.

M. Dimova, S. Dimova, D. Vasileva: Numerical Investigation of a New Class of Waves in an Open Nonlinear Heat-Conducting Medium,
Cent. Eur. J. Math., 11 (2013) , 1375-1391, IF 0.440.

S. Dimova, M. Dimova, D. Vasileva: Structures and waves in a nonlinear heat-conducting medium,
Springer Proc. in Math. & Statistics, 45 (2013), 157-184.

N. Kutev, N. Kolkovska, M. Dimova: Global existence to generalized Boussinesq equation with combined power-type nonlinearities,
Journal of Mathematical Analysis and Applications, 410 (2014), 427-444, IF 1.050.

N. Kolkovska: Four-level conservative finite-difference schemes for Boussinesq paradigm equation,
AIP Conference Proceedings, 1561 (2013), 68-74, SJR 0.161.

V. S. Gerdjikov, M. D. Todorov: On the effects of sech-like potentials on Manakov solitons,
AIP Conference Proceedings, 1561 (2013), 75-83, SJR 0.161.

N. Kutev, N. Kolkovska, M. Dimova: Global solvability to generalized Boussinesq equation with Bernoulli type nonlinearities via nonstandard potential well method,
AIP Conference Proceedings, 1561 (2013), 297-308, SJR 0.161.

L. M. Kovachev , D. A. Georgieva, V. N. Serkin: Parametric solitons in isotropic media,
AIP Conference Proceedings, 1561 (2013), 289-296, SJR 0.161.

N. C. Papanicolaou, M. A. Christou, A. C. Polycarpou: Numerical characterization of nematic liquid crystal microstructures under applied electric fields,
AIP Conference Proceedings, 1561 (2013), 309-317, SJR 0.161

I. Bazhlekov, D. Vasileva: Numerical simulation of drop coalescence in the presence of drop soluble surfactant,
AIP Conference Proceedings, 1561 (2013), 333-346, SJR 0.161.

C.I.Christov, M.D.Todorov: Investigation of the Long-Time Evolution of Localized Solutions of a Dispersive Wave System,
Discrete and Continuous Dynamical Systems, Supplement 2013, 139-148.

M. D. Todorov: Finite-Difference Implementation of Conserved Properties of Vector NLSE,
Journal of Geometry and Symmetry in Physics 32 (2013), 51-60, SJR 0.438.

M. Todorov, Role of the Nonlinear Coupling in the Collision Dynamics of Quasi-Particles Governed by Vector NLSE,
chapter in B. Aneva, G. Grahovsky, R. Ivanov, D. Mladenov (Eds.), International Conference on Integrability, Recursion Operators and Soliton Interactions, Sofia, 247-274, Avangard Prima, Sofia, (2014), ISBN: 978-619-160-313-8.

A. Kyuldjiev, V. Gerdjikov, M. Todorov, Asymptotic Behavior of Manakov Solitons: Effects of Shallow and Wide Potential Wells and Humps,
in A. Slavova (Ed.), Mathematics in Industry, Cambridge Scholars Publ., 356-371, 2014.

D. Vasileva, N. Kolkovska, Investigation of Two Numerical Schemes for 2D Boussinesq Paradigm Equation in a Moving Frame Coordinate System,
in A. Slavova (Ed.), Mathematics in Industry, Cambridge Scholars Publ., 289-305, 2014.

N. Kutev, N. Kolkovska, M. Dimova, Global Solvability and Finite Time Blow Up of the Solution to Sixth Order Boussinesq Equation,
in A. Slavova (Ed.), Mathematics in Industry, Cambridge Scholars Publ., 274-288, 2014.

D. Georgieva, Numerical and analytical analysis of some nonlinear physical problems (in Bulgarian), PhD Thesis, TU Sofia, 2014.

V.S. Gerdjikov, M.D. Todorov, A.V. Kyuldjiev: Asymptotic Behavior of Manakov Solutions: Effects of Potential Wells and Humps,
under review in Mathematics and Computers in Simulation (arXiv: 1408.0230 [math-ph] 4 Aug 2014).

D. Georgieva, L. Kovachev, Energy Transfer between Two Filaments due to Degenerate Four-photon Parametric Process,
under review in Journal of Optic Society of America B (IF 2.21), (arXiv:1404.3578 [physics.optics] 14 Apr 2014).

L. Kovachev, D. Georgieva, Four-photon Parametric Mixing and Interaction between Filaments,
AMiTaNS’14 AIP Conf. Proc. 1629 (2014), 146-153, SJR 0.162.

N. Kutev, N. Kolkovska, M. Dimova, Global Behavior of the Solutions to Boussinesq Type Equation with Linear Restoring Force,
AMiTaNS’14 AIP Conf. Proc. 1629 (2014), 172-185, SJR 0.162.

D. Vasileva, A Numerical Investigation of Stability of 1D Soliton Solutions of Boussinesq Paradigm Equation in the 2D Case,
AMiTaNS’14 AIP Conf. Proc. 1629 (2014), 207-216, SJR 0.162.

N.C. Papanicolaou, M.A. Christou, A.C. Polycarpou, Numerical Analysis of Nematic Liquid Crystals as Applied to Tunable Antennas,
AMiTaNS’14 AIP Conf. Proc. 1629 (2014), 444-451, SJR 0.162.

I. Bazhlekov, D. Vasileva, Numerical Simulation of Drop Coalescence in the Presence of Inter-Phase Mass Transfer,
accepted in NMA'14, Lecture Notes in Computer Science (SJR 0.332), August 2014.

N. Kolkovska, Error Estimates of Four Level Conservative Finite Difference Schemes for Multidimensional Boussinesq Equation,
accepted in FDM 2014, Lecture Notes in Computer Science (SJR 0.332), September 2014.

V. Gerdjikov, A. Kyuldjiev, M. Todorov, Manakov Solitons and Effects of External Potential Wells,
submitted to Discrete and Continuous Dynamical Systems (SJR 1.39), Supplement 2015.