User:Tao: Difference between revisions

**Cubic NLS on $\mathbb {R}$**
Description
Equation
Fields	{{{fields}}}
Data class
Basic characteristics
Structure	Completely integrable
Nonlinearity	semilinear
Linear component	Schrodinger
Critical regularity
Criticality	mass-subcritical;; energy-subcritical;; scattering-critical
Covariance	-
Theoretical results
LWP	for
GWP	for
Related equations
Parent class	NLS
Special cases	-
Other related	KdV, mKdV

Revision as of 14:53, 7 August 2006

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

I'm experimenting with a equation template. On the right you see a typical example of this template in action.

@@ Line 6: / Line 6: @@
 {{equation
-  | name = Cubic NLS on R
+  | name = Cubic NLS on <math>\R</math>
-  | equation = <math>iu_t + u_xx = \pm |u|^2 u</math>
+  | equation = <math>iu_t + u_{xx} = \pm |u|^2 u</math>
-  | data = <math>u \in H^s(\R \to \C)</math>
+  | data = <math>u \in H^s(\R \to \mathbb{C})</math>
   | hamiltonian = [[Completely integrable]]
   | linear = [[free Schrodinger equation|Schrodinger]]
@@ Line 17: / Line 17: @@
   | lwp = <math>H^s(\R)</math> for <math>s \geq 0</math>
   | gwp = <math>H^s(\R)</math> for <math>s \geq 0</math>
+ | parent = [[NLS]]
+ | special = -
+ | related = [[KdV]], [[mKdV]]
 }}
 I'm experimenting with a [[Template:Equation|equation template]].  On the right you see a typical example of this template in action.

Description
Equation	$iu_{t}+u_{xx}=\pm \|u\|^{2}u$
Fields	{{{fields}}}
Data class	$u\in H^{s}(\mathbb {R} \to \mathbb {C} )$
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