TY - JOUR
T1 - Applying theory of bridges et al to second-order isospectral AKNS equations
AU - Han, Songmei
AU - Hu, Weipeng
AU - Deng, Zichen
AU - Zhang, Jinfu
PY - 2010/8
Y1 - 2010/8
N2 - 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.
AB - 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.
KW - Multi-symplectic scheme
KW - Second-order isospectral AKNS equations
KW - Solitons
UR - http://www.scopus.com/inward/record.url?scp=77957954024&partnerID=8YFLogxK
M3 - 文章
AN - SCOPUS:77957954024
SN - 1000-2758
VL - 28
SP - 525
EP - 529
JO - Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University
JF - Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University
IS - 4
ER -