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In this paper, it is shown that the solutions of the Toda lattice in Flaschka's form with a self-consistent integral-type source can be found by the inverse scattering problem for the discrete Sturm–Liouville operator. Moreover, the conditions are obtained under which the Toda lattice with an integral-type source has pure soliton solutions. The results can be used in modeling special types of electric transmission lines.
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Cabada et al. (2010) studied this question.
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