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arXiv · 2610.39829

Klein-Gordon-Born-Infeld equations driven by mixed local-nonlocal operators

Nicolò Cangiotti·Maicol Caponi·Alberto Maione·Enzo Vitillaro
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Abstract

In this paper we study a class of Klein-Gordon-Born-Infeld systems in which the classical Laplacian appearing in the matter equation is replaced by a mixed local-nonlocal operator, whose nonlocal part is allowed to be nonpositive definite according to a real parameter. Both the approximate and the exact Born-Infeld field equations are considered in parallel. After making the functional framework explicit, we identify a range of real parameters for which infinitely many radially symmetric standing waves exist, obtained as Mountain Pass critical points of the associated reduced energy functionals. The mixed local-nonlocal operator reduces to the classical Laplacian as the nonlocal weight vanishes, and is motivated, in the spirit of effective field theories, by nonlocal corrections to the matter dispersion relation.

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Nicolò Cangiotti, Maicol Caponi, Alberto Maione, Enzo Vitillaro. 2026-10-29. Klein-Gordon-Born-Infeld equations driven by mixed local-nonlocal operators. https://arxiv.org/abs/2610.39829

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