Abstract—A new kind of integrable couplings of soliton hierarchies with self-consistent sources associated with sl(4) was presented. Based upon this method, two new integrable couplings associated with Li soliton hierarchy and BKK soliton hierarchy with self-consistent sources were obtained by making use of loop algebra sl(4) respectively. Meanwhile, their Hamiltonian structures of the integrable couplings of Li and BKK soliton hierarchies were obtained by making use of variational identity . The method in this study can be applied to other soliton hierarchies with self-consistent sources.

Index Terms—Li soliton hierarchy, self-consistent sources, integrable couplings, BKK soliton hierarchy

Sixing Tao is with the Department of Mathematics, Shangqiu Normal University, Shangqiu, 476000, China (tel: 86-13781680641; email: taosixing@163.com).
Hui Shi is with the Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu, 476000, China (tel: 86-13523157699, email: shihui529@126.com).

Cite:Sixing Tao and Hui Shi, "Two New Integrable Couplings of Soliton Hierarchies with Self-consistent Sources," International Journal of Applied Physics and Mathematics vol. 1, no. 1, pp. 72-77, 2011.