Nonlinear Wave Equation Explorer

equation coefficients

cubic

-2.34

quadratic

-3.65

linear

0

constant

1

initial peak separation

2.5

solution range

10

show mesh

quality

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medium

high

plot type

2D

3D

Explore the solutions of nonlinear wave equations of the form

∂

t,t

ϕ=

∂

x,x

ϕ+a

3

ϕ

+b

2

ϕ

+cϕ+d

. Varying the coefficients in the polynomial can lead to vastly different behavior in the solutions—including some that become infinite or exhibit various other pathologies. Fairly little is known about these solutions. Sometimes they are quite simple, but often they appear to show the same kind of complexity seen in systems like cellular automata. A particular example of these nonlinear wave equations is Wolfram's equation.