1984/12/01 by T. Yoneyama
Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · doi:10.1143/ptp.72.1081
crossref issued 1984/12/01 · crossref published 1984/12/01 · crossref published-print 1984/12/01 · openalex publication_date 1984/12/01 · crossref created 2005/12/14 · crossref deposited 2017/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04 · crossref indexed 2026/07/25
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.