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

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


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


  • Ashok Das; Ziemowit Popowicz (2005). "A nonlinearly dispersive fifth order integrable equation and its hierarchy" (PDF). Journal of Nonlinear Mathematical Physics. 12 (1): 105–117. arXiv:nlin/0404049. Bibcode:2005JNMP...12..105D. doi:10.2991/jnmp.2005.12.1.9.

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