Optimal decay and asymptotic behavior of solutions to a non-local perturbed KdV equation
Résumé
We consider the KdV equation with an additional non-local perturbation term given in terms of the Hilbert transform. We find the asymptotic expansion when |x| → +∞ of solutions to this equation corresponding to initial conditions which decays as 1/ 1 + |x|^ 2. Moreover, we prove that this spatially-decaying is optimal even if the initial datais a fast-decay funcion.
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