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Scattering operator for the fourth order nonlinear Schrödinger equation. (English) Zbl 1479.35792

Summary: We study the fourth order nonlinear Schrödinger equation \[i{\partial }_tu-\frac{1}{4}\partial_x^4u=f(u) ,\quad (t,x)\in \mathbb{R}\times \mathbb{R},\] where \(f(u)\) is the power nonlinearity of order \(p>5\). The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
81U99 Quantum scattering theory
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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