Integrable generalizations of the two new soliton hierarchies of AKNS and KN types associated with $so(3,\mathbb{R})$

Chun-Xia Li; Shou-Feng Shen; Wen-Xiu Ma; Shui-Meng Yu

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arXiv · 1406.1326

Integrable generalizations of the two new soliton hierarchies of AKNS and KN types associated with $so(3,\mathbb{R})$

Chun-Xia Li·Shou-Feng Shen·Wen-Xiu Ma·Shui-Meng Yu

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Abstract

The two matrix spectral problems of Ablowitz-Kaup-Newell-Segur (AKNS) and Kaup-Newell (KN) types associated with so(3,R) are generalized. The corresponding hierarchies of generalized soliton equations are derived by the standard procedure using the zero curvature formulation. Recursion operators and bi-Hamiltonian structures are explicitly constructed for the resulting two generalized soliton hierarchies of AKNS and KN types, which shows their Liouville integrability.

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Chun-Xia Li, Shou-Feng Shen, Wen-Xiu Ma, Shui-Meng Yu. 2014-06-05. Integrable generalizations of the two new soliton hierarchies of AKNS and KN types associated with $so(3,\mathbb{R})$. https://arxiv.org/abs/1406.1326

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