We consider the nonlinear ion acoustic wave induced by orbiting charged space debris objects in the plasma environment generated at the Low Earth Orbital (LEO) region. The generated nonlinear ion acoustic wave is shown to be governed by a forced Korteweg-de Vries (fKdV) equation with the forcing function dependent on the charged space debris function. For a specific relationship between the forcing debris function and the nonlinear ion acoustic wave, the forced KdV equation turns out to be a completely integrable system; where the debris function obeys a definite nonholonomic constraint. A special exact accelerated soliton solution (velocity of the soliton changes over time whereas its amplitude remains constant) has been derived for the ion acoustic wave for the first time. On the other hand, the amplitude of the solitonic debris function varies with time, and its shape changes during the propagation. Approximate ion acoustic solitary wave solutions with time varying amplitudes and velocities have been derived for different types of weakly localized charged debris functions. Possible applications of the obtained results in space plasma physics are stated along with future directions for research.
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This work has been carried out with partial financial support from the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST MISiS \(( K4-2018-061)\), implemented by a governmental decree dated 16th of March 2013, N 211. Abhik Mukherjee gratefully acknowledges late Prof. Anjan Kundu for scintillating discussions in this field. Abhik Mukherjee would also like to thank Ms. Aurna Kar for checking the grammars and literary aspects of the manuscript. Siba Prasad Acharya acknowledges the Department of Atomic Energy (DAE) of Government of India for financial support during this work through institute fellowship scheme as well.
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Mukherjee, A., Acharya, S.P. & Janaki, M.S. Dynamical study of nonlinear ion acoustic waves in presence of charged space debris at Low Earth Orbital (LEO) plasma region. Astrophys Space Sci 366, 7 (2021). https://doi.org/10.1007/s10509-020-03914-2
- Forced Korteweg-de Vries equation
- Complete integrability
- AKNS-type lax pair
- Nonholonomic constraint
- Debris function
- Pinned accelerated soliton