Two new integrable couplings of the soliton hierarchies with self-consistent sources

doi:10.1088/1674-1056/19/10/100303

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100303-100303.doi: 10.1088/1674-1056/19/10/100303

Two new integrable couplings of the soliton hierarchies with self-consistent sources

夏铁成

Department of Mathematics, Shanghai University, Shanghai 200444, China

收稿日期:2009-10-26 修回日期:2010-03-29 出版日期:2010-10-15 发布日期:2010-10-15
基金资助:
Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800), the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806), the Shanghai Leading Academic Discipline Project (Grant No. J50101), the Key Disciplines of Shanghai Municipality (Grant No. S30104), and the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159).

Two new integrable couplings of the soliton hierarchies with self-consistent sources

Xia Tie-Cheng(夏铁成)^†

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2009-10-26 Revised:2010-03-29 Online:2010-10-15 Published:2010-10-15
Supported by:
Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800), the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806), the Shanghai Leading Academic Discipline Project (Grant No. J50101), the Key Disciplines of Shanghai Municipality (Grant No. S30104), and the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159).

摘要/Abstract

摘要： A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with $\widetilde{sl}$(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra $\widetilde{sl}$(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.

Abstract: A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with $\widetilde{sl}$(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra $\widetilde{sl}$(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.

Key words: TC hierarchy, generalized Burgers hierarchy, self-consistent sources, integrable couplings, loop algebra

中图分类号: (Linear algebra)

02.10.Ud

02.30.Ik (Integrable systems) 05.45.Yv (Solitons)

夏铁成. Two new integrable couplings of the soliton hierarchies with self-consistent sources[J]. 中国物理B, 2010, 19(10): 100303-100303.

Xia Tie-Cheng(夏铁成). Two new integrable couplings of the soliton hierarchies with self-consistent sources[J]. Chin. Phys. B, 2010, 19(10): 100303-100303.

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Two new integrable couplings of the soliton hierarchies with self-consistent sources

Two new integrable couplings of the soliton hierarchies with self-consistent sources

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