The Kaup–Kupershmidt equation (named after David J. Kaup and Boris Abram Kupershmidt) is the

nonlinear In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...

fifth-order

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

u_t = u_+10u_u+25u_u_x+20u^2u_x = \frac16 (6u_+60uu_+45u_x^2+40u^3)_x.

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

\partial_x^3 + 2u\partial_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

External links

* Partial differential equations Integrable systems {{mathanalysis-stub