Interacting Korteweg-de Vries Equations and Attractive Soliton Interaction
1984; Oxford University Press; Volume: 72; Issue: 6 Linguagem: Inglês
10.1143/ptp.72.1081
ISSN1347-4081
Autores Tópico(s)Advanced Fiber Laser Technologies
ResumoBy 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.
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