title: Soliton evolution and radiation loss for the sine-Gordon equation.
abstract: An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.
authors.affiliation: Department of Mathematics and Statistics, The King's Buildings, University of Edinburgh, Edinburgh, Scotland, United Kingdom, EH9 3JZ. noel@maths.ed.ac.uk
authors.forename: N F
authors.initials: NF
authors.lastname: Smyth
authors.forename: A L
authors.initials: AL
authors.lastname: Worthy