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Creators/Authors contains: "Koch, Herbert"

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  1. ; (, Publications mathématiques de l'IHÉS)
    For both the cubic Nonlinear Schrödinger Equation (NLS) as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension we consider the set of N--soliton states, and their associated multisoliton solutions. We prove that (i) this set is a uniformly smooth manifold, and (ii) the$$\mathbf {M}_{N}$$ M N states are uniformly stable in H^s for each s>-1/2. One main tool in our analysis is an iterated Bäcklund transform, which allows us to nonlinearly add a multisoliton to an existing soliton free state (the soliton addition map) or alternatively to remove a multisoliton from a multisoliton state (the soliton removal map). The properties and the regularity of these maps are extensively studied. 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; ; (, Annales Scientifiques de l'École Normale Supérieure)
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