87 citations · 192 across the 23 of their papers we have counts for
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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…
Focusing mKdV Breather Solutions with Nonvanishing Boundary Conditions by the Inverse Scattering Method
Miguel A. Alejo
Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain the square k^2 of a focusing modified Korteweg-de Vries (mKdV) breather solution with non zero…
Discrete conservation laws and the convergence of long time simulations of the mKdV equation
Carlos Gorria, Miguel A. Alejo, Luis Vega
Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solution…
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…