Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV-sine-Gordon equation

摘要

The main results of this paper are two numerical algorithms of a physically-interesting mKdV-sine-Gordon model. One is a numerical scheme to calculate the 3-periodic wave solutions (expressed in terms of special theta functions) of the model under consideration. The other is an efficient numerical scheme to numerically solve the model through the interpretation of Backlund transformations as discrete time integrable systems.