Oleg A Kharshiladze, Jemal Rogava and Vasily Yu Belashov
Tbilisi State University, Georgia
Kazan Federal University, Russia
Scientific Tracks Abstracts: J Astrophys Aerospace Technol
Investigation of evolution and interaction of solitary waves and pulses (wave packets) is very actual problem in
different fields of physics especially when the medium is non-uniform and its properties depend on time. In this case,
as a model, we use the generalized non-linear Schrödinger (GNLS) equation, which describes the waves in a plasma,
fiber and planar optical waveguides, taking into account the inhomogeneity and non-stationary of a propagation
medium. Earlier we have shoved analytically that the GNLS equation can have stable and quasi-stable solutions of the
soliton and breather types and also unstable solutions which disperse with time. In this paper we study the evolution
and interaction of the envelop solitons numerically. At simulation the Fourier Splitting Method for the GNLS
equation was used and the specially developed implicit scheme of finite-difference method was used for investigation
of soliton like structures propagation in non-uniform and non-stationary medium. Numerical modeling showed that
inhomogeneity of medium changes the parameters of the envelop solitons such as their amplitudes, velocities and
their quantity that is caused by their non-elastic interaction in inhomogeneous medium. Non-stationary medium
changes a form of pulses and affects their spectral features. Changes of modulation of the parameters of medium
make possible variation of character of non-elastic interaction at solitons attraction repulsion. Obtained results can be
useful in numerous applications in plasma physics, nonlinear optics and in many other fields of physics.
1. 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.
2. 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 Press 18:90.
Oleg A Kharshiladze is Associate Professor at Physics Department of Tbilisi State University. He is involved in International Scientific group, working on Analytical and Numerical analysis of Ionospheric and Magnetospheric processes (turbulence, shear flows, BBF and others).