Vasily Yu Belashov*

Institute of Physics, Kazan Federal University, Kazan, Russia

*Corresponding Author: Vasily Yu Belashov, Institute of Physics, Kazan Federal University, Kazan, Russia.

Received: October 07, 2021; Published: December 10, 2021

Abstract

The formation, structure, stability and dynamics of the multidimensional solitons forming on the low-frequency branch of oscillations in plasma for cases when  and  are studied. In first case, for  the FMS wa­ves are excited, and their dyna­mics under conditions ,  ne­­ar the cone of , is described by the GKP equa­ti­on for mag­netic field  with due acco­unt of the high order dispersive correc­tion defined by values of plasma para­me­ters and angle . In ano­ther case, the dynamics of the finite-am­plitude Alfvén waves propagating near-to-parallel to B is described by the 3-DNLS equation for . To study the stability of mul­tidimensional solitons in both cases the method of investigation of the Hamiltonian bounding with deformation conserving mo­men­tum by solving the variation problem is used. To study evolution of solitons and the­ir collision dynamics the proper equations are integrated numerical­ly using the codes specially developed. As a result, it was obtained that in both cases for single solitons on a level with wave spreading and collapse the formation of multidimensional solitons may be observed. These results may be also interpreted in terms of self-focusing phenomenon for the FMS and Alfvén waves’ beam as stationary beam formation, scattering and self-focusing of beam. The soliton collisions on a level with known elastic interaction can lead to formation of complex structures including the multisoliton bound states. For all cases the problem of soliton dynamics including all stages of their evolution and collision dynamics is investigated in detail.

Keywords: Plasma; GKP Equation; 3-DNLS Equation; Dynamics; 2D Solutions; 3D Solutions; Structure; Stability; Multidimensional Solitons

References

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Citation

Citation: Shaik Sumayyah Banu., et al. “Aetiology of Meningitis in Paediatric Age Group at a Tertiary Care Centre in Hyderabad, India - A Cross Sectional Study". Acta Scientific Clinical Case Reports 2.1 (2022): 09-14.

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Copyright: © 2022 Shaik Sumayyah Banu., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.