Combined breathing–kink modes in the FPU lattice

Combined breather–kink modes have been observed in several systems. Here we show that in the FPU lattice, small amplitude breathing–kink modes are three-soliton solutions of an associated mKdV equation. Since this is integrable, the modes can be constructed using the Bäcklund transform. As well as finding explicit solutions, we consider the stability of the combined mode using variational techniques and illustrate stability for some parameter values and instability for others.