Abstract:
We prove in this paper the stability and asymptotic stability in H 1 of a decoupled sum of N solitons for the subcritical generalized KdV equations The proof of the stability result is based on energy arguments and monotonicity of the local L 2 norm. Note that the result is new even for p=2 (the KdV equation). The asymptotic stability result then follows directly from a rigidity theorem in [16].
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Received: 8 October 2001 / Accepted: 2 July 2002 Published online: 14 October 2002
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Martel, Y., Merle, F. & Tsai, TP. Stability and Asymptotic Stability for Subcritical gKdV Equations. Commun. Math. Phys. 231, 347–373 (2002). https://doi.org/10.1007/s00220-002-0723-2
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DOI: https://doi.org/10.1007/s00220-002-0723-2