Applying theory of bridges et al to second-order isospectral AKNS equations

Bridges et al in Refs. 1 and 2 extended the symplectic algorithm for finite dimensional Hamilton system to the multi-symplectic algorithm for infinite dimensional Hamilton system; this extension is generally acknowledged to play an important role in studying the structure preserving algorithm of a complex nonlinear problem. Applying the extension of Bridges et al to second-order isospectral AKNS equations, section 1 of the full paper, by introducing suitable orthogonal momenta, derives multi-symplectic formulations with several conservation laws according to the Hamilton variational principle. Section 2 deduces a semi-implicit multi-symplectic scheme, which is equivalent to the Preissmann Box scheme. Section 3 derives the single-soliton of the second-order isospectral AKNS equations; q and r can be computed with eq. (21). Numerical simulation results are given in Figs. 1, 2 and 3 and Table 1. These results show preliminarily that the multi-symplectic scheme is very good in two respects: (1) high precision; (2) long-time stable numerical behaviour and good conservation.