ITERATIVE IMPLICIT SCHEMES FOR THE 2-DIMENSIONAL AND 3-DIMENSIONAL SINE-GORDON EQUATION

[摘要] In this paper, ring wave solutions to the Sine-Gordon equation u(rr) + {(m - 1)/r}u(r) - u(rr) = sin u, in two and three dimensions are investigated by numerical computations. The combined approach of linearization and finite differences is used to get iterative implicit schemes for solving the Since-Gordon equation. The accuracy and efficiency of the schemes are discussed. The numerical results show that each expanding wave exhibits a return effect. Collision experiments for expanding and shrinking concentric ring waves are carried out. The results show that the solutions posses quasi soliton properties.

[发布日期] 1991-04-04

[关键词] SINE-GORDON EQUATION;LINEARIZATION;FINITE DIFFERENCES;ITERATIVE SCHEMES;RING WAVES;SOLITONS