Abstract
A Backlund transformation in the bilinear form is presented for the Toda equation. The Backlund transformation generates an important class of nonlinear evolution equations that exhibits N-soliton solutions. The equation reduces, in the special cases, to the Toda equation itself, the nonlinear self-dual network equation, the equation describing a Volterra system and a discrete Korteweg·de Vries equation. Physical meanings and properties of solitons of these equations are examined in detail. Special solutions are also given to the generated equation. Moreover, a relation between the Backlund transformation and the inverse scattering method, and a nonlinear transformation relating the Toda equation and the generated equation are presented.
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