Displaying similar documents to “Stability of solitary waves for nonlinear Schrödinger equation”

Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations

Fabrice Planchon (1999)

Journées équations aux dérivées partielles

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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 B ˙ 2 n 2 - 2 p , ( 𝐑 n ) , when the nonlinearity is of type u p , for p 𝐍 . 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.