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.
