Article Contents
Article Contents

# Long-term stability for kdv solitons in weighted Hs spaces

• 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.

Mathematics Subject Classification: Primary: 35Q53, 35B35; Secondary: 37K40, 35B40, 37K45, 35Q51.

 Citation:

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