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Homoclinics, rogue waves and breathers in nonlinear lattice wave equations
We prove the existence of rogue waves and breathers in nonlinear lattice wave equations including the nonlinear Klein--Gordon and the FPUT lattice (with added local forces). The main feature of our lattice wave equation is that the kinetic part $\frac{\mathrm{d}^2}{\mathrm{d}t^2}$ is multiplied by a
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