Kaup–Kupershmidt equation

The Kaup–Kupershmidt equation is the nonlinear fifth-order partial differential equation

:$u\_t\; =\; u\_\{xxxxx\}+10u\_\{xxx\}u+25u\_\{xx\}u\_x+20u^2u\_x\; =\; frac16\; (6u\_\{xxxx\}+60uu\_\{xx\}+45u\_x^2+40u^3)\_x.$

It is the first equation in a hierarchy of integrable equations with Lax operator

:$partial\_x^3\; +\; 2upartial\_x\; +\; u\_x.$

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