Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws

This paper investigates the stability and dynamical behavior of soliton solutions in generalized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We establish the existence of stable multisoliton configurations using variational methods and demonstrate their stability under...

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Bibliographic Details
Published inNonlinear analysis (Vilnius, Lithuania) Vol. 30; no. 4; pp. 620 - 637
Main Author Díaz Palencia, José Luis
Format Journal Article
LanguageEnglish
Published Vilnius University Press 12.05.2025
Subjects
nonlinear Klein–Gordon equation
soliton stability
topological invariants
variational methods
variational methods
nonlinear Klein–Gordon equation
soliton stability
topological invariants
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ISSN1392-5113
2335-8963
DOI10.15388/namc.2025.30.41967

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Summary:This paper investigates the stability and dynamical behavior of soliton solutions in generalized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We establish the existence of stable multisoliton configurations using variational methods and demonstrate their stability under small perturbations through energy estimates and topological considerations. Furthermore, we explore topological invariants (particularly, the topological charge) in preventing certain types of instabilities and ensuring the long-term persistence of solitons.
ISSN:1392-5113
2335-8963
DOI:10.15388/namc.2025.30.41967