Modified scattering for the nonlinear Klein–Gordon equation

Ballesteros M, Franco Cordova G, Naumkin I, Vázquez AV (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Partial Differential Equations and Applications Springer International Publishing

Book Volume: 7

Article Number: 28

Journal Issue: 3

DOI: 10.1007/s42985-026-00390-1

Abstract

We consider the modified scattering problem for the nonlinear Klein–Gordon equation with cubic nonlinear interactions in one spatial dimension (Formula presented.) for μ∈R. We show that for any small real valued initial data w0,w1 low-regularity weighted Sobolev spaces there exists a unique modified final state W+∈L∞ such that the corresponding solution exhibits a logarithmic phase correction as t→∞. Our proof is based on the Factorization Technique. We present more simple and robust method for the proof of this result based on the Factorization Technique and on the L2 - estimates for the transformed evolution operators, which considerably simplifies the proof of the asymptotics of solutions.

Authors with CRIS profile

Gerardo Franco Cordova Professur für Mathematik (Mathematische Physik)

Involved external institutions

National Autonomous University of Mexico / Universidad Nacional Autónoma de México (UNAM) MX Mexico (MX) Instituto Tecnologico del Valle de Morelia MX Mexico (MX)

How to cite

APA:

Ballesteros, M., Franco Cordova, G., Naumkin, I., & Vázquez, A.V. (2026). Modified scattering for the nonlinear Klein–Gordon equation. Partial Differential Equations and Applications, 7(3). https://doi.org/10.1007/s42985-026-00390-1

MLA:

Ballesteros, Miguel, et al. "Modified scattering for the nonlinear Klein–Gordon equation." Partial Differential Equations and Applications 7.3 (2026).

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