The Nonlinear BK System: Structure, Stability And Interaction Of Multidimensional Solitons In Complex Dispersive Media | 106242
Journal of Astrophysics & Aerospace Technology
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The structure, stability and interaction of the multidimensional nonlinear waves and solitons forming on the lowfrequency
branch of oscillations in complex dispersive media are studied analytically and numerically on the basis
of the nonlinear Belashov-Karpman (BK) system which includes the Kadomtsev-Petviashvili (GKP), the nonlinear
schrodinger (NLS) and the derivative nonlinear Schrodinger (DNLS) classes of equations and takes into account the
generalizations relevant to various complex physical media including space plasma, atmosphere, hydrosphere and other
complex dispersive media, associated with the effects of high-order dispersion corrections, influence of dissipation and
instabilities. This is consistent representation of both early known and new original results obtained by authors and also
some generalizations in theory of the nonlinear waves and solitons in complex dispersive media. The stability analysis
of solutions is based on study of transformational properties of the Hamiltonian of the system. The structure of possible
multidimensional solutions is investigated using the methods of qualitative analysis of proper dynamical systems and
analysis of the solutions??? asymptotics. The interaction of multidimensional solitons is studied numerically. So, we have
considered the nonlinear wave processes in different complex physical media using general approach basing on the
general BK system and have obtained the results on dynamics of the 2D and 3D solitons for different physical systems
from uniform positions. Some applications of obtained results in plasmas and atmosphere are presented.
1. Belashov V Yu, Belashova E S and Kharshiladze O A (2018) Nonlinear wave structures of the soliton and vortex
types in complex continuous media: theory, simulation, applications. Lecture Notes of TICMI. Tbilisi University
2. Belashov V Yu, Belashova E S and Kharshiladze O A (2018) Classification of multidimensional solitary solutions
of the GKP equation by use of qualitative and asymptotic analysis. Journal of Physical Chemistry and Biophysics
3. Belashov V Yu and Belashova E S (2018) Hamiltonian analysis of stability and classification of multidimensional
nonlinear wave structures of soliton type in space plasma. Journal of Astrophysics and Aerospace Technology
4. Belashov V Yu, Kharshiladze O A and Rogava J (2018) Interaction of the multidimensional NLS solitons in nonuniform
and nonstationary medium: modeling and stability problem. Journal of Astrophysics and Aerospace
5. Belashov V Yu, Belashova E S and Kharshiladze O A (2018) Problem of stability of multidimensional solutions
of the BK class equations in space plasma. Advances in Space Research 62:65-70.
Vasily Yu Belashov has completed his PhD in Radio Physics and DSci in Physics and Mathematics. He is Chief Scientist and Professor at the Kazan Federal University. He was Coordinator of studies on the Intern. Program “Solar Terminator” (1987-1992), and took part in the Intern programs WITS/WAGS and STEP. He is author of 340 publications including 8 monographs. His main books are “Solitary Waves in Dispersive Complex Media. Theory, Simulation, Applications”, “Solitons: Theory, Simulation, Applications”.