Csobo, ElekGenoud, FrancoisOhta, MasahitoRoyer, Julien2019-10-242019-10-242019-10-242019-12-1510.1016/j.jde.2019.08.015https://infoscience.epfl.ch/handle/20.500.14299/162296WOS:000489568700013In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike the unperturbed case, a noteworthy difficulty here arises from the possible non-unitarity of the semigroup generating the corresponding linear evolution. We then show that the equation is Hamiltonian and we establish several stability/instability results for its standing waves. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability. (C) 2019 Elsevier Inc. All rights reserved.MathematicsMathematicsnonlinear klein-gordon equationstanding wavesorbital stabilitydelta potentialschrodinger-equationsolitary wavesstrong instabilityorbital stabilitysolitonstext::journal::journal article::research article