Brian Pigott, Sarah Raynor
Published 2014-10-25Version 1
In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restriction is due to a lack of global control of the unweighted perturbation.
Asymptotic Stability for KdV Solitons in Weighted Spaces via Iteration
Asymptotic stability in the energy space for dark solitons of the Landau-Lifshitz equation
Kink dynamics in the $φ^4$ model: asymptotic stability for odd perturbations in the energy space
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