Breather solution for a Klein-Gordon equation with periodically varying coefficients

Breather solution for a Klein-Gordon equation
s(x) d_t^2 u = d_x^2 u + s(x) (q_0 - epsilon^2) u + r u^3
with x, t, u = u(x,t) in R and s = s(x) a periodic step function.
For more details see:
doi.org/10.100...
Simulation carried out by Ch. Hamster using Dedalus (dedalus-projec...)