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}
}
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]. 
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Showing 1-10 of 21 references

Asymptotic stability of solitons for subcritical generalized KdV equations

  • Y. Martel, F. Merle
  • Arch. Rational Mech. Anal. 157, 219–254
  • 2001
Highly Influential
11 Excerpts

A Liouville Theorem for the critical generalized Korteweg–de Vries equation

  • Y. Martel, F. Merle
  • J. Math. Pures Appl. 79, 339–425
  • 2000
Highly Influential
6 Excerpts

On the stability of KdV multi-solitons

  • J. H. Maddocks, R. L. Sachs
  • Comm. Pure Appl. Math. 46, 867–901
  • 1993
Highly Influential
6 Excerpts

Lyapunov stability of ground states of nonlinear dispersive evolution equations

  • M. I. Weinstein
  • Comm. Pure. Appl. Math. 39, 51–68
  • 1986
Highly Influential
4 Excerpts

Well-posedness and scattering results for the generalized Korteweg–de Vries equation via the contraction principle

  • C. E. Kenig, G. Ponce, L. Vega
  • Comm. Pure Appl. Math. 46, 527–620
  • 1993
Highly Influential
4 Excerpts

Instability of solitons for the critical generalized Korteweg–de Vries equation

  • Y. Martel, F. Merle
  • Geom. Funct. Anal. 11, 74–123
  • 2001

Some results on the scattering of weakly interacting solitons for nonlinear Schrödinger equations

  • G. S. Perelman
  • 1997
2 Excerpts

On the stability of solitary waves for nonlinear Schrödinger equations

  • V. S. Buslaev, G. S. Perelman
  • ed., Transl.,
  • 1995
2 Excerpts

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