The Kaup–Kupershmidt equation (named after David J. Kaup and Boris Abram Kupershmidt) is the
nonlinear
In mathematics and science, a nonlinear 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, mathematicians, and many other ...
fifth-order
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
:
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 mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which starts with the Korteweg–de Vries equation.
Details
Let T be translation operator defined on real valued functions as T(g)(x)=g(x+1). Let \mathca ...
in which the Lax operator has order 2.
References
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External links
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Partial differential equations
Integrable systems
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