Breathers for a Relativistic Nonlinear Wave Equation

Abstract

 A new class of one-dimensional relativistic nonlinear wave equations with a singular δ-type nonlinear term is considered. The sense of the equations is defined according to the least-action principle. The energy and momentum conservation is established. The main results are the existence of time-periodic finite-energy solutions, the existence of global solutions and soliton-type asymptotics for a class of finite-energy initial data.