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# A P ] 7 D ec 2 00 1 Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations

@inproceedings{Martel2001AP, title={A P ] 7 D ec 2 00 1 Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations}, author={Yvan Martel and Frank Merle and Timothy P. Tsai}, year={2001} }

- Published 2001

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 ut + (uxx + u)x = 0 (1 < p < 5). The proof of the stability result is based on energy arguments and monotonicity of the local L2 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].Â