Creation and annihilation of solitons in the system described by the Korteweg-de Vries equation with a self-consistent source

The inverse scattering method for the one-dimensional Schrodinger operator on a straight line is used to derive solutions for the Korteweg-de Vries equation with a self-consistent source which describe creation and annihilation of solitons. The reason for this phenomenon is the dependence on time of the points of the discrete spectrum of the Schrodinger operator, or, more precisely, their vanishing in the process of evolution.

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