Korteweg-de Vries equation: Difference between revisions

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The <span class="SpellE">KdV</span> equation has been studied [[Korteweg-de Vries equation on R|on the line]], [[Korteweg-de Vries equation on T|on the circle]], and [[Korteweg-de Vries equation on the half-line|on the half-line]].
The <span class="SpellE">KdV</span> equation has been studied [[Korteweg-de Vries equation on R|on the line]], [[Korteweg-de Vries equation on T|on the circle]], and [[Korteweg-de Vries equation on the half-line|on the half-line]].
The KdV equation is the first non-trivial equation on the [[KdV hierarchy]].


[[Category:Equations]]
[[Category:Equations]]

Revision as of 05:50, 28 July 2006

The Korteweg-de Vries (KdV) equation is

The factor of 6 is convenient for reasons of complete integrability, but can easily be scaled out if desired.

The equation is completely integrable, and has infinitely many conserved quantities. Indeed, for each non-negative integer k, there is a conserved quantity which is roughly equivalent to the H^k norm of u.

The KdV equation has been studied on the line, on the circle, and on the half-line.

The KdV equation is the first non-trivial equation on the KdV hierarchy.