Homoclinics, rogue waves and breathers in nonlinear lattice wave equations
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 d2/dt2 is multiplied by a non-constant function 1/d(t) such that gaps in the spectrum of 1/d(t)d2/dt2 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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BibTeX
@misc{henninger2026homoclinics,
title = {{Homoclinics, rogue waves and breathers in nonlinear lattice wave equations}},
author = {Julia Henninger and Wolfgang Reichel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26456},
eprint = {2609.26456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26456},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Homoclinics, rogue waves and breathers in nonlinear lattice wave equations
AU - Julia Henninger
AU - Wolfgang Reichel
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26456
UR - https://arxiv.org/abs/2609.26456
AB - 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 d^2/dt^2 is multiplied by a non-constant function 1/d(t) such that gaps in the spectrum of 1/d(t)d^2/dt^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.
ER -