Kaup–Kupershmidt equation
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The Kaup–Kupershmidt equation (named after David J. Kaup and Boris Abram Kupershmidt) is the nonlinear fifth-order partial differential equation
- [math]\displaystyle{ 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. }[/math]
It is the first equation in a hierarchy of integrable equations with the Lax operator
- [math]\displaystyle{ \partial_x^3 + 2u\partial_x + u_x, }[/math] .
It has properties similar (but not identical) to those of the better-known KdV hierarchy in which the Lax operator has order 2.
References
- Ashok Das; Ziemowit Popowicz (2005). "A nonlinearly dispersive fifth order integrable equation and its hierarchy". Journal of Nonlinear Mathematical Physics 12 (1): 105–117. doi:10.2991/jnmp.2005.12.1.9. Bibcode: 2005JNMP...12..105D. http://www.sm.luth.se/~norbert/home_journal/electronic/121art5.pdf.
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