2014/10/25 by Brian Pigott, Pigott, Brian, Sarah Raynor +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1410.6872
arxiv created 2014/10/25 · arxiv updated 2014/10/28
In this paper, we reconsider the well-known result of Pego-Weinstein \citeMR1289328 that soliton solutions to the Korteweg-deVries equation are asymptotically stable in exponentially weighted spaces. In this work, we recreate this result in the setting of modern well-posedness function spaces. We obtain asymptotic stability in the exponentially weighted space via an iteration argument. Our purpose here is to lay the groundwork to use the I-method to obtain asymptotic stability below H1, which will be done in a second, forthcoming paper \citePR. This will be possible because the exponential approach rate obtained here will defeat the polynomial loss in traditional applications of the I-method \citeMR1995945, \citeMR1951312, \citepigottorb.