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arXiv · 2609.26456

Homoclinics, rogue waves and breathers in nonlinear lattice wave equations

Julia Henninger·Wolfgang Reichel
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Abstract

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 non-constant function $\frac{1}{d(t)}$ such that gaps in the spectrum of $\frac{1}{d(t)}\frac{\mathrm{d}^2}{\mathrm{d}t^2}$ open wide enough to include the spectrum of the spatial linear operator. We find solutions as critical points of an indefinite functional using a saddle-point method combined with concentration-compactness arguments. In case of temporally $T$-periodic coefficients and under identical assumptions as for rogue waves, the same variational method also provides existence of breather solutions whose temporal period is an arbitrary prescribed integer multiple of $T$.

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Julia Henninger, Wolfgang Reichel. 2026-09-22. Homoclinics, rogue waves and breathers in nonlinear lattice wave equations. https://arxiv.org/abs/2609.26456

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