Asymptotic stability of solitary waves for nonlinear Schrödinger equations
Galina Perelman (2002-2003)
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Galina Perelman (2002-2003)
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We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space , when the nonlinearity is of type , for . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.