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Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs. (English) Zbl 1439.35336

Summary: The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations is obtained by symmetry and reversibility arguments.

MSC:

35L71 Second-order semilinear hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35R02 PDEs on graphs and networks (ramified or polygonal spaces)
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