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Error bounds for the (KdV)/(KP-I) and (gKdV)/(gKP-I) asymptotic regime for Nonlinear Schrödinger type Equations

Abstract : We consider the (KdV)/(KP-I) asymptotic regime for the Nonlinear Schrödinger Equation with a general nonlinearity. In a previous work, we have proved the convergence to the Korteweg-de Vries equation (in dimension 1) and to the Kadomtsev-Petviashvili equation (in higher dimensions) by a compactness argument. We propose a weakly transverse Boussinesq type system formally equivalent to the (KdV)/(KP-I) equation in the spirit of the work of Lannes and Saut, and then prove a comparison result with quantitative error estimates. For either suitable nonlinearities for (NLS) either a Landau-Lifshitz type equation, we derive a (mKdV)/(mKP-I) equation involving cubic nonlinearity. We then give a partial result justifying this asymptotic limit.
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Contributor : David Chiron <>
Submitted on : Friday, October 18, 2013 - 11:25:44 AM
Last modification on : Monday, October 12, 2020 - 10:27:31 AM
Long-term archiving on: : Sunday, January 19, 2014 - 4:25:37 AM

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David Chiron. Error bounds for the (KdV)/(KP-I) and (gKdV)/(gKP-I) asymptotic regime for Nonlinear Schrödinger type Equations. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2014, 31 (6), pp.1175-1230. ⟨hal-00874581⟩

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