Scattering for the Quartic Generalised Korteweg-de Vries Equation
نویسنده
چکیده
We show that the quartic generalised KdV equation ut + uxxx + (u )x = 0 is globally wellposed for data in the critical (scale-invariant) space Ḣ −1/6 x (R) with small norm (and locally wellposed for large norm), improving a result of Gruenrock [8]. As an application we obtain scattering results in H x(R) ∩ Ḣ −1/6 x (R) for the radiation component of a perturbed soliton for this equation, improving the asymptotic stability results of Martel and Merle [11].
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