Stability Problem And Simulation Of Interaction Of The Multidimensional NLS Solitons In Non-uniform And Non-stationary Media | 106246
Journal of Astrophysics & Aerospace Technology
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Investigation of dynamics of multidimensional electromagnetic (EM) waves in plasma, such as 2D and 3D envelop
solitons, is very actual problem. The interaction sufficiently changes the characteristics of the waves and background
EM field in the region of interaction. Problem of the dynamics and stability becomes more complicated if it is
necessary to take into account an influence of different dispersive and nonlinear inhomogeneities and nonstationary
parameters of medium on the soliton structure and evolution. In this case the problem reduces to the generalized
nonlinear schrodinger (GNLS) equation for the amplitude of the EM field with coefficient functions having spatial
and temporal inhomogeneities. The analysis of stability of the multidimensional GNLS solitons was based on the
method of study of transformational properties of the Hamiltonian of the system developed by authors earlier for the
BK class of the equations. As a result we have found the conditions of existence of the multidimensional stable GNLS
soliton solutions. At simulation the Fourier splitting method for the GNLS equation was used taking into account
the inhomogeneities of coefficient functions of the equation. Implicit scheme of finite-difference method was used
for investigation of soliton propagation in non-uniform and nonstationary medium. Numerical modeling showed
that inhomogeneity of medium changes the amplitudes of solitons and nonlinear EM waves, their velocities of
propagation, their quantity that is caused by their nonelastic interaction in inhomogeneous medium. Nonstationary
medium changes a form of impulse and affects its spectral features. Changes of modulation of the parameters of
medium make possible variation of character of nonelastic interaction at solitons attraction-repulsion.
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. 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
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”.