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Global self-similar solutions of a class of nonlinear Schrödinger equations. (English) Zbl 1180.35493

Summary: For a certain range of the value \(p\) in the nonlinear term \(|u|^{p}u\), we mainly study the global existence and uniqueness of global self-similar solutions to the Cauchy problem for some nonlinear Schrödinger equations by harmonic analysis.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C05 Solutions to PDEs in closed form
35A25 Other special methods applied to PDEs
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References:

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