Scattering for the quartic generalised Korteweg-de Vries equation

Details Scattering for the quartic generalised Korteweg-de Vries equation Scattering for the quartic generalised Korteweg-de Vries equation

2006-05-14

arxiv.org/abs/math/0605357v1

Mathematics

Analysis of PDEs

28 pages, no figures, submitted, J. Diff. Eq

Scientific paper

We show that the quartic generalised KdV equation $$ u_t + u_{xxx} + (u^4)_x = 0$$ is globally wellposed for data in the critical (scale-invariant) space $\dot H^{-1/6}_x(\R)$ with small norm (and locally wellposed for large norm), improving a result of Gr\"unrock. As an application we obtain scattering results in $H^1_x(\R) \cap \dot H^{-1/6}_x(\R)$ for the radiation component of a perturbed soliton for this equation, improving the asymptotic stability results of Martel and Merle.

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