Korteweg-de Vries equation: Difference between revisions

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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 <span class="SpellE">H^k</span> norm of u.
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 <span class="SpellE">H^k</span> norm of u.


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 R^+|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 R^+|on the half-line]].


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

Revision as of 05:25, 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 [[Korteweg-de Vries equation on R|on the line], [[Korteweg-de Vries equation on T|on the circle], and on the half-line.