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

Abstract

This paper investigates the stability and dynamical behavior of soliton solutions in gen-eralized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We estab-lish the existence of stable multisoliton configurations using variational methods and demonstratetheir stability under small perturbations through energy estimates and topological considerations.Furthermore, we explore topological invariants (particularly, the topological charge) in preventingcertain types of instabilities and ensuring the long-term persistence of solitons.