Document Zbl 1212.35020

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Nonexistence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in two space dimensions. (English) Zbl 1212.35020

Differ. Integral Equ. 18, No. 3, 325-335 (2005).

Summary: In this paper, the asymptotic behavior in time of solutions for the nonlinear Schrödinger equation with the quadratic nonlinearity \(\lambda | u| ^2\) with \(\lambda \in \mathbb C\setminus \{0\}\) in two space dimensions is studied. The nonexistence of asymptotically free solutions for this equation is proved.

Cited in 10 Documents

MSC:

35B40	Asymptotic behavior of solutions to PDEs
35P25	Scattering theory for PDEs
35Q55	NLS equations (nonlinear Schrödinger equations)

Keywords:

nonlinear Schrödinger equation; global behavior

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