2010/12/23 by Miguel A. Alejo, Miguel Á. Alejo, Alejo, Miguel A. +4
Mathematics · Physics and Astronomy · #35Q51 #35Q53 #37K10 #37K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #msc:35Q51 #msc:35Q53 #msc:37K10 #msc:37K40
paper · pdf · doi:10.48550/arxiv.1012.5290
19 pages, final version incorporating referee's comments. To appear in TAMS
openalex publication_date 2010/12/23 · arxiv created 2011/01/22 · arxiv updated 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingly simple and combines the Gardner transform, which links the Gardner and KdV equations, together with the Martel-Merle-Tsai and Martel-Merle recent results on stability and asymptotic stability in the energy space, applied this time to the Gardner equation. As a by-product, the results of Maddocks-Sachs and Merle-Vega are improved in several directions.