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Prog. Theor. Phys. Supplement No.59 (1976) pp. 64-100

[ Full Text PDF : FREE ACCESS (2219K) ]

A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice

Ryogo Hirota and Junkichi Satsuma*

Department of Mathematics and Physics, Ritsumeikan University, Kyoto
*Department of Applied Mathematics and Physics, Kyoto University, Kyoto

(Received April 20, 1976)

Abstract:

A Bäcklund 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 Bäcklund transformation and the inverse scattering method, and a nonlinear transformation relating the Toda equation and the generated equation are presented.


URL : http://ptp.ipap.jp/link?PTPS/59/64/
DOI : 10.1143/PTPS.59.64

[ Full Text PDF : FREE ACCESS (2219K) ] Citation:

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