We consider the nonlinear ion-acoustic wave induced by the orbiting charged space debris in the plasma environment generated at Low Earth Orbital (LEO) region. The generated nonlinear ion-acoustic wave is shown to be governed by the forced Korteweg-de Vries 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 to be a completely integrable system where the debris function obeys a definite non-holonomic 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 propagation. Approximate ion-acoustic solitary wave solutions with time-varying amplitude and velocity, have been derived for different weak localized charged debris functions. Possible applications of the obtained results in space plasma physics are stated along with future the direction of research.
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