Existence and multiplicity of soliton-like solutions for a class of nonlinear Klein–Gordon equations

We establish some stability properties for a set of stationary solutions to a class of nonlinear wave equations of the type Klein-Gordon, where the nonlinear term is given by a function on the plane having a unique global minimum and a singularity. These solutions represent wave packets which do not spread and can be regarded as quasiparticles for the system, exhibiting a soliton-like behavior. Their stability properties are guaranteed by a topological constraint and are studied using variational methods.