The Rosenau–Hyman equation or K(n,n) equation is a KdV-like equation having compacton solutions. This nonlinear partial differential equation is of the form
| n) | |
| u | |
| xxx |
=0.
The equation is named after Philip Rosenau and James M. Hyman, who used in their 1993 study of compactons.
The K(n,n) equation has the following traveling wave solutions:
u(x,t)=\left(
| 2cn | |
| a(n+1) |
\sin2\left(
| n-1 | |
| 2n |
\sqrt{a}(x-ct+b)\right)\right)1/(n-1),
u(x,t)=\left(
| 2cn | |
| a(n+1) |
| ||||
| \sinh |
\sqrt{-a}(x-ct+b)\right)\right)1/(n-1),
u(x,t)=\left(
| 2cn | |
| a(n+1) |
\cosh2\left(
| n-1 | |
| 2n |
\sqrt{-a}(x-ct+b)\right)\right)1/(n-1).