Michail Todorov，graduated in 1984 and received a PhD degree in 1989 from the St. Klimem Ohridski University of Sofia， Bulgaria. Since 1990， he has been Associate Professor and Full Professor （2012） with the Department of Applied Mathematics and Computer Science by the Technical University of Sofia， Bulgaria. He has worked as a Senior Research Fellow in the Joint Institute for Nuclear Research at Dubna， Russia （2004） and as a Visiting Professor， a Visiting Scholar and a Visiting Consultant in the University of Texas at Arlington， TX， USA （2008，2009 and 2011） and Texas A&M University at Commerce， TX USA （2011）， Sabbatical Professor at Southeastern Louisiana University at Hammond，LA， USA （2013） and Embrie-Riddle Auonautical University， Daytona Beach，FL，USA （2017）.
目錄：
Preface
Acknowledgements
Author biography
1 Two-dimensional Boussinesq equation． Boussinesq paradigm and soliton solutions
1．1 Boussinesq equations． Generalized wave equation
1．2 Investigation of the long-time evolution of localized solutions of a dispersive wave system
1．3 Numerical implementation of Fourier-transform method for generalized wave equations
1．4 Perturbation solution for the 2D shallow-water waves
1．5 Boussinesq paradigm equation and the experimental measurement
1．6 Development and realization of efficient numerical methods， algorithms and scientific software for 2D nonsteady Boussinesq paradigm equation． Comparative analysis of the results References
2 Systems of coupled nonlinear SchrSdinger equations． Vector Schrodinger equation
2．1 Conservative scheme in complex arithmetic for vector nonlinear Schrodinger equations
2．2 Finite-difference implementation of conserved properties of the vector nonlinear Schrodinger equation （VNLSE）
2．3 Collision dynamics of circularly polarized solitons in nonintegrable VNLSE
2．4 Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector nonlinear Schr6dingcr equation
2，5 Repelling soliton collisions in vector nonlinear Schr6dinger equation with negative cross modulation
2．6 On the solution of the system of ordinary differential equations governing the polarized stationary solutions of vector nonlinear Schr6dinger equation
2．7 Collision dynamics of elliptically polarized solitons in vector nonlinear Schr6dinger equation
2．8 Collision dynamics of polarized solitons in linearly coupled vector nonlinear Schr6dinger equation
2．9 Polarization dynamics during takeover collisions of solitons in vector nonlinear Schr6dinger equation
2．10 The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled vector nonlinear Schr6dinger equation
2．11 Vector nonlinear Schr6dinger equation with different cross-modulation rates
2．12 Asymptotic behavior of Manakov solitons
2．13 Manakov solitons and effects of external potential wells and humps References
3 Ultrashort optical pulses． Envelope dispersive equations
3．1 On a method for solving of multidimensional equations of mathematical physics
3．2 Dynamics of high-intensity ultrashort light pulses at some basic propagation regimes
3．3 （3 I）D nonlinear Schr6dinger equation
3．4 （3 I）D nonlinear envelope equation （NEE）
3．5 Summary of the studies
References
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