Computational study of nonlinear waves in a generalised nonlinear mass-in-mass Fermi-Pasta-Ulam-Tsingou chain

We present numerical simulations of discrete breather in the mass-in-mass Fermi-Pasta-Ulam-Tsingou chain in which each external particle is connected both to its nearest neighbours and to an internal oscillator. We consider the case where both types of interaction have nonlinear components. An asymptotic reduction to the Nonlinear Schrödinger (NLS) equation recovers approximate solitary waves. In some cases the asymptotic reduction instead leads to a Complex Ginzburg-Landau equation. Our numerical results illustrates that the system supports stable stationary breathers and combined breatherkink (or wobbling-kink) solutions, as well as an unstable breather and breather-kink solutions.