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• W3082805083 abstract "Author(s): Koch, Herbert; Tataru, Daniel | Abstract: For both the cubic Nonlinear Schr quot;odinger Equation (NLS) as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension we consider the set ${bf M}_N$ of pure $N$-soliton states, and their associated multisoliton solutions. We prove that (i) the set ${bf M}_N$ is a uniformly smooth manifold, and (ii) the ${bf M}_N$ states are uniformly stable in $H^s$, for each $sg-frac12$. One main tool in our analysis is an iterated Backlund 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." @default.
• W3082805083 created "2020-09-08" @default.
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• W3082805083 date "2020-08-30" @default.
• W3082805083 modified "2023-09-27" @default.
• W3082805083 title "Multisolitons for the cubic NLS in 1-d and their stability" @default.
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