The perturbed sine-Gordon breather equation integrated by Riemann's method

Research paper by E. Mann

Indexed on: 01 Jun '96Published on: 01 Jun '96Published in: Theoretical and Mathematical Physics


A general first-order perturbation solution in the neighborhood of the unperturbed breather solution is given for the nonlinear perturbed sine-Gordon equation. The inhomogeneous linear-hyperbolic differential equation is solved by Riemann's method. No methods of inverse scattering theory are used for the determination of the Riemann function. Instead, the Bäcklund transformation and a novel inversion relation are applied. The Riemann function may be expressed in terms of two-variable Lommel functions. It is shown that the thus-formulated Riemann function has the correct symmetry, unlike the discrete part. As an example, the asymptotic solution for a low-amplitude breather under a constant perturbation is given, showing that plane waves are radiated to both sides of the breather.