A numerical calculation of a weakly non-local solitary wave: the ϕ4breather

The breather of the phi 4 field theory decays by radiation to infinity. The concept of a solitary wave is still useful, however, because alpha , the amplitude of the 'far field' radiation, is exponentially small in in , the breather amplitude. (The phrase 'weakly non-local' in the title means that the quasisoliton has non-zero but very tiny amplitude as mod x mod to infinity .) The author introduces novel numerical methods to compute phi 4 breathers. He calculates solutions both on a finite, spatially periodic interval and on x in (- infinity , infinity ).