87 citations · 192 across the 23 of their papers we have counts for
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math.AP2011★ 8 cited
Well-posedness and stability results for the Gardner equation
Miguel A. Alejo
In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of…
math.AP2011★ 8 cited
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation
Miguel A. Alejo, Claudio Muñoz, Luis Vega
Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingl…