Kaup–Kupershmidt equation

The Kaup–Kupershmidt equation (named after David J. Kaup and Boris Abram Kupershmidt) is the nonlinear fifth-order partial differential equation

$u_t = u_{xxxxx}%2B10u_{xxx}u%2B25u_{xx}u_x%2B20u^2u_x = \frac16 (6u_{xxxx}%2B60uu_{xx}%2B45u_x^2%2B40u^3)_x.$

In addition to it being the first equation in a hierarchy of integrable equations with Lax operator

$\partial_x^3 %2B 2u\partial_x %2B u_x,$

it is also the second non-trivial equation in the KdV hierarchy - the first of which is the KdV equation.

References

Das, Ashok; and Ziemowit Popowicz (2005). "A nonlinearly dispersive fifth order integrable equation and its hierarchy" (PDF). Journal of Nonlinear Mathematical Physics 12 (1): 105–117. doi:10.2991/jnmp.2005.12.1.9. http://www.sm.luth.se/~norbert/home_journal/electronic/121art5.pdf.

External links

Weisstein, Eric W., "Kupershmidt Equation" from MathWorld.

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