User:Tao

Terence Tao

For contact details, papers, etc. see my home page.

Equation template

Cubic NLS on $\mathbb {R}$

Description
Equation	$iu_{t}+u_{xx}=\pm |u|^{2}u$
Fields	$u:\mathbb {R} \times \mathbb {R} \to \mathbb {C}$
Data class	$u(0)\in H^{s}(\mathbb {R} )$
Basic characteristics
Structure	completely integrable
Nonlinearity	semilinear
Linear component	Schrodinger
Critical regularity	$L^{2}(\mathbb {R} )$
Criticality	mass-subcritical; energy-subcritical; scattering-critical
Covariance	-
Theoretical results
LWP	$H^{s}(\mathbb {R} )$ for $s\geq 0$
GWP	$H^{s}(\mathbb {R} )$ for $s\geq 0$
Related equations
Parent class	NLS
Special cases	-
Other related	KdV, mKdV

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