Particle stability in nonlinear scalar field theory

Using the direct Lyapunov method for distributed systems, the problem of stability of particlelike solutions of the equation of a scalar field with logarithmic nolinearity is solved. It is shown that nonlinearities of the Heaviside function type, which ensure the existence of exact regular solutions for the Klein-Gordon equation, are not a very fruitful approach because of the mathematical difficulties encountered in studying the stability of such solutions. © 1980 Plenum Publishing Corporation.