Abstract—Enlargement of Lie super algebra B(0, 1) was given firstly. Then nonlinear super integrable couplings of the super classical Boussinesq hierarchy based upon this enlarged matrix Lie super algebra were constructed secondly. And its super Hamiltonian structures were established by using super trace identity thirdly. As its reduction, special integrable couplings of classical Boussinesq hierarchy were obtained finally.

Index Terms—Lie super algebra, super integrable couplings,super classical Boussinesq hierarchy, super Hamiltonian structures.

Sixing Tao is with School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, China (email: taosixing@163.com).
Hui Shi is with School of Physics and Electronic Information, Shangqiu Normal University, Shangqiu, 476000, China.

Cite: Sixing Tao, Hui Shi, "Nonlinear Super Integrable Couplings of Super Classical Boussinesq Hierarchy," International Journal of Applied Physics and Mathematics vol. 5, no. 3, pp. 177-184, 2015.