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Prog. Theor. Phys. Vol. 72 No. 6 (1984) pp. 1081-1088

Interacting Korteweg-de Vries Equations and Attractive Soliton Interaction

Tohru Yoneyama

Department of Physics, Shizuoka University, Shizuoka 422

(Received August 27, 1984)

Abstract:

By a physically natural way, the Korteweg-de Vries (KdV) equation is extended to obtain interacting (Int) KdV equations. They can also be regarded as results of a decoupling of the original KdV equation. By introducing new operators, solutions of the Int KdV equations are obtained starting with the exact KdV N-soliton solution. The KdV N-soliton solution is decomposed into a simple sum of the solutions of the Int KdV equations, each of which is regarded as a soliton suffering much deformation when another soliton (other solitons) comes near in space. These single solitons as classical waves interact attractively and eventually become apart in space without losing their identities. The relation to the inverse scattering method is also discussed in detail. Further, “partical” Lax forms corresponding to the Int KdV equations are shown.

URL : http://ptp.ipap.jp/link?PTP/72/1081/
DOI : 10.1143/PTP.72.1081

[ Full Text PDF : FREE ACCESS (397K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Journal of the Physical Society of Japan 60 (1991) pp. 798-809 :

   Hierarchies of Coupled Soliton Equations. I

   Ryogo Hirota and Yasuhiro Ohta

2. Journal of the Physical Society of Japan 73 (2004) pp. 3275-3284 :

   Multi-Component Generalizations of Four Integrable Differential-Difference Equations: Soliton Solutions and Bilinear Bäcklund Transformations

   Jun-Xiao Zhao, Xing-Biao Hu and Ryogo Hirota

3. Progress of Theoretical Physics Vol. 78 No. 5 (1987) pp. 1022-1050 :

   Solitons in Interaction

   Benno Fuchssteiner

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