## 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

### Keywords:

Cauchy problem; harmonic analysis
Full Text:

### References:

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