Long-term stability for kdv solitons in weighted Hs spaces

Brian Pigott; Sarah Raynor

doi:10.3934/cpaa.2017020

Article Contents

2017, Volume 16, Issue 2: 393-416. Doi: 10.3934/cpaa.2017020

This issue Previous Article Singular periodic solutions for the p-laplacian ina punctured domain Next Article Center conditions for generalized polynomial kukles systems

Long-term stability for kdv solitons in weighted H^s spaces

Brian Pigott^1, and
Sarah Raynor^2,

1.
Department of Mathematics Wofford College, 429 North Church Street, Spartanburg, SC 29303
2.
Department of Mathematics and Statistics, Wake Forest University, P.O. Box 7388, Winston Salem, NC 27109

Author Bio: E-mail address: pigottbj@wofford.edu
^* Corresponding author: Sarah Raynor.
^* Corresponding author: Sarah Raynor.

Received: November 30, 2015

Revised: September 30, 2016

Published: August 2017

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Abstract

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.

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

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References

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