Neha Patil (Editor)

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

u t = u x x x x x + 10 u x x x u + 25 u x x u x + 20 u 2 u x = 1 6 ( 6 u x x x x + 60 u u x x + 45 u x 2 + 40 u 3 ) x .

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

∂ x 3 + 2 u ∂ x + u x , .

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

References

Kaup–Kupershmidt equation Wikipedia
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