Kaup–Kupershmidt equation

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

$u_t = u_{xxxxx}+10u_{xxx}u+25u_{xx}u_x+20u^2u_x = \frac16 (6u_{xxxx}+60uu_{xx}+45u_x^2+40u^3)_x.$

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

$\partial_x^3 + 2u\partial_x + u_x,$ .

Ii has properties similar (but not identical) to those of the better-known KdV hierarchy in which the Lax operator has order 2.

References

• Das, Ashok; 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.

External links

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