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

xx

,

u

xxx

,

u

xxxx

)

and

u

tt

=f(u,

u

x

,

u

xx

,

u

xxx

,

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.