Combined breathing-kink modes in the FPU lattice

► We show that the beta-FPU lattice can be reduced to the mKdV pde. ► We construct moving three-soliton kink-breather solutions of the mKdV equation. ► These are found by use of the Backlund transform. ► We show how the variational form of the FPU system is connected to that of the mKdV equation. ► We find both stable and unstable modes in the original FPU lattice.