WOLFRAM|DEMONSTRATIONS PROJECT

Some Partial Differential Equations with Chaotic Solutions

​
equation
21.
(2,0)
u
(t,x)0.1
(1,0)
u
(t,x)u(t,x)-
(0,2)
u
(t,x)-
3
u(t,x)
plot
2D
3D
range
This Demonstration considers some partial differential equations with chaotic solutions of the form
u
t
=f(u,
u
x
,
u
u
xx
,
u
u
xxx
,
u
u
xxxx
)
and
u
tt
=f(u,
u
x
,
u
u
xx
,
u
u
xxx
,
u
u
xxxx
,
u
t
)
. Sprott and others [1] found this set by an extensive search; the plots are shown in order of increasing complexity and are not necessarily optimally elegant. Periodic boundary conditions are chosen and the condition
∂
t
u(t,x)=0
is used for the
u
tt
equations. Different equations can be selected by scrolling down the list.