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Zbl 0832.35132
Ohta, Masahito
Blow-up solutions and strong instability of standing waves for the generalized Davey-Stewartson system in $\bbfR\sp 2$. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 63, No.1, 111-117 (1995). ISSN 0246-0211

Summary: We study the instability of standing waves $e^{i\omega t}\varphi_\omega(x)$ for the equation $$iu_t+ \Delta u+ a|u|^{p- 1} u+ E_1(|u|^2) u= 0\tag1$$ in $\bbfR^2$, where $\varphi_\omega$ is a ground state. We prove that if $a(p- 3)> 0$, then there exist blow-up solutions of (1) arbitrarily close to the standing wave.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35B40 Asymptotic behavior of solutions of PDE
35Q51 Solitons

Keywords: standing wave; blow-up solutions

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