Example
The Korteweg–de Vries equation is
It can be reformulated as the Lax equation
with
- (a Sturm–Liouville operator)
where all derivatives act on all objects to the right. This accounts for the infinite number of first integrals of the KdV equation.
Read more about this topic: Lax Pair
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)