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degase
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There are 6 letters in DEGASE ( A1D2E1G2S1 )
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In mathematical physics, the Degasperis–Procesi equation* * * * * * u * * t * * * − * * u * * x * x * t * * * + * 2 * κ * * u * * x * * * + * 4 * u * * u * * x * * * = * 3 * * u * * x * * * * u * * x * x * * * + * u * * u * * x * x * x * * * * * * {\displaystyle \displaystyle u_{t}-u_{xxt}+2\kappa u_{x}+4uu_{x}=3u_{x}u_{xx}+uu_{xxx}} * is one of only two exactly solvable equations in the following family of third-order, non-linear, dispersive PDEs: * * * * * * * u * * t * * * − * * u * * x * x * t * * * + * 2 * κ * * u * * x * * * + * ( * b * + * 1 * ) * u * * u * * x * * * = * b * * u * * x * * * * u * * x * x * * * + * u * * u * * x * x * x * * * , * * * * {\displaystyle \displaystyle u_{t}-u_{xxt}+2\kappa u_{x}+(b+1)uu_{x}=bu_{x}u_{xx}+uu_{xxx},} * where * * * * κ * * * {\displaystyle \kappa } * and b are real parameters (b=3 for the Degasperis–Procesi equation). It was discovered by Degasperis and Procesi in a search for integrable equations similar in form to the Camassa–Holm equation, which is the other integrable equation in this family (corresponding to b=2); that those two equations are the only integrable cases has been verified using a variety of different integrability tests. Although discovered solely because of its mathematical properties, the Degasperis–Procesi equation (with * * * * κ * > * 0 * * * {\displaystyle \kappa >0} * ) has later been found to play a similar role in water wave theory as the Camassa–Holm equation. |