2008/05/28 by Yair Zarmi, Zarmi, Yair
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.48550/arxiv.0805.4281
arxiv created 2008/05/28 · openalex publication_date 2008/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations: The (inte-grable) Normal Form for KdV-type solitons, which obey the usual infinity of KdV-conservation laws, and an auxiliary equation that describes the contribution of obstacles to asymptotic inte-grability, which arise from the second order onwards. The analysis has been carried through the third order in the expansion. Within that order, the solution of the auxiliary equation is a con-served quantity.