A stable time–space Jacobi pseudospectral method for two-dimensional sine-Gordon equation

Abstract

In this article, we present the stability analysis and approximate solutions of circular ring solitary solitons wave for (2 + 1)-dimensional nonlinear sine-Gordon equation using time–space pseudospectral method. Error bounds on discrete $$L_{2}$$-norm and Sobolev norm $$(H^{p})$$ are presented. The discretization of the problem using proposed method leads a system of nonlinear equations, which are solved using Newton–Raphson method. Further, a study is carried out to investigate the effects of dissipative term in sine-Gordon equation, which presence forms circular ring solitons. To support the theoretical results, the proposed method is tested for two problems, single circular ring solitary soliton waves and the collision of four circular ring solitary soliton waves and numerical results are presented.