A generalized AKNS hierarchy, bi-Hamiltonian structure, and Darboux transformation

作者：Zhaqilao^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(6): 2319-2332.

DOI：10.1016/j.cnsns.2011.10.010

• Darboux transformation
• Soliton solution
• Generalized AKNS hierarchy
• Bi-Hamiltonian structure

A new generalized AKNS hierarchy is presented starting from a 4 x 4 matrix spectral problem with four potentials. Its generalized bi-Hamiltonian structure is also investigated by using the trace identity. Moreover, the special coupled nonlinear equation, the coupled KdV equation, the KdV equation, the coupled mKdV equation and the mKdV equation are produced from the generalized AKNS hierarchy. Most importantly, a Darboux transformation for the generalized AKNS hierarchy is established with the aid of the gauge transformation between the corresponding 4 x 4 matrix spectral problem, by which multiple soliton solutions of the generalized AKNS hierarchy are obtained. As a reduction, a Darboux transformation of the mKdV equation and its new analytical positon, negaton and complexiton solutions are given.

• 出版日期2012-6
• 单位内蒙古师范大学