Korteweg-de Vries equation: Difference between revisions
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The '''Korteweg-de Vries (KdV) equation''' is | The '''Korteweg-de Vries (KdV) equation''' is | ||
<center><math>u_t + u_xxx + 6uu_x = 0.</center> | <center><math>u_t + u_xxx + 6uu_x = 0.</math></center> | ||
The factor of 6 is convenient for reasons of [[complete integrability]], but can easily be scaled out if desired. | The factor of 6 is convenient for reasons of [[complete integrability]], but can easily be scaled out if desired. | ||
Revision as of 05:24, 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.
