The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation

This paper presents the dual reciprocity boundary element method (DRBEM) for solving two-dimensional sine-Gordon (SG) equation. The integral equation formulation employs the fundamental solution of the Laplace equation, and hence a domain integral arises in the boundary integral equation. Furthermore, the time derivatives are approximated by the time-stepping method, and the domain integral also appears from these approximations. The domain integral is transformed into boundary integral by using the dual reciprocity method (DRM). The linear radial basis function (RBF) is employed for DRM. The dynamics of line solitons and ring solitons of circular and elliptic shapes are studied. Numerical results are presented for some problems involving line and ring solitons to demonstrate the usefulness and accuracy of this approach.