Abstract
Modulational instability and long time evolutions of monochromatic initial waves are investigated numerically for a modified Toda lattice incorporating external linear elastic force. The inclusion of this elastic substrate effect causes a drastic change in wave modulations. Numerical consequences are discussed in terms of the usual nonlinear Schrödinger equation as well as a discrete envelope equation. The amplitude dependence of the modulational instability is suggested to be attributed to a discreteness effect. Generations of localised structures remniscent of what is called “chaotic breathers (CBs)” are observed for initial waves with high wavenumbers due to the existence of the elastic substrate force. Mergings of breathers into a single CB as well as eventual dampings of it into a thermalised state are observed. CBs can persist for a long time without damping when the effect of the substrate force is sufficiently large.
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