Physical dynamics of quasi-particles in nonlinear wave equations
arXiv:nlin/0612005 · doi:10.1016/j.physleta.2007.08.038
Abstract
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.
10 pages, 3 figures (6 images); v2: revised and improved the presentation, updated the references, fixed typos; v3: corrected a few minor mistakes and typos, version accepted for publication in Phys. Lett. A