Abstract
According to a recent theorem proved by Derrick, no absolutely stable time-independent particle-like solution of finite energy is obtainable from a large class of Lorentz-covariant scalar wave theories. We study a solvable nonlinear scalar wave theory and derive a rigorous metastable particlelike solution of finite energy, a quasistatic solution having a rate of dissolution which is free to be arbitrarily small relative to the associated particle rest mass. Derrick's theorem notwithstanding, the specific example presented here suggests that particlelike quasistatic solutions to a nonlinear scalar wave theory may still be of some relevancy to meson field physics, where no absolutely stable but instead metastable elementary particles are present.
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