A semi‐adaptive split‐cosine scheme for the sine‐Gordon equation

This talk concerns the numerical solution of the nonlinear sine‐Gordon equation in rectangular large‐area Josephson junctions. An application of the adaptive method of lines leads to a system of second‐order nonlinear ordinary differential equations. The system is approximated by a nonlinear recurrence relation. Strang's splitting is then introduced for establishing a highly effective and stable semi‐adaptive scheme. The novel new method offers an efficient way in the solitary wave solution approximations. A stability analysis is presented. Straightforward numerical demonstrations on ring solitons up to higher time levels are given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)