Breather solutions are quite rare for the nonlinear wave equations. Up to rescaling, the only spatially homogeneous model known to admit such solutions is the sine-Gordon equation. In contrast, it is expected to be different for the nonlinear wave equation in inhomogeneous media modelling by $/rho(x)u_{tt}-(/mu(x)u_x)_x=f(x,u)$. With this spatially inhomogeneous model, for the first time we discover the existence of many breather solutions. This is a joint work with Professor C.E. Wayne.
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