Nonlinear chain

The nonlinear coupled lattice in the animation satisfies the differential equation
d2/dt2 x n = x n + g L xn + h V(xn),
where L is the discrete nearest neighbor Laplacian, V is a nonlinear cubic potential and g,h are real coupling constants. The chain is 4 periodic in the x and y directions.
It is a space discretisation of a nonlinear wave equation on a torus.
The simulation uses a discrete Euler method, we see actually the evolution of a coupled map lattice.
In this specific case each step is given by a map on the 32-dimensional Euclidean space.


© 1999, Oliver Knill ,