Semi-direct sums of Lie algebras and continuous integrable couplings

By Wenxiu Ma, Xi-Xiang Xu, Yufeng Zhang. 2006

264 citations recorded by the source corpus.

A relation between semi-direct sums of Lie algebras and integrable couplings of continuous soliton equations is presented, and correspondingly, a feasible way to construct integrable couplings is furnished. A direct application to the AKNS spectral problem leads to a novel hierarchy of integrable couplings of the AKNS hierarchy of soliton equations. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards complete classification of integrable systems.

Subfields: Spectroscopy, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ca3b0f92be10f5e8c4a2337c0b38fbb732ba6f02

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In Spectroscopy

1. Wenxiu Ma
2. Xi-Xiang Xu
3. Yufeng Zhang
4. Jin-Yun Yang
5. Xing Lü
6. Yuan Zhou

In Statistical and Nonlinear Physics

1. Wenxiu Ma
2. Xi-Xiang Xu
3. Yufeng Zhang
4. Jin-Yun Yang
5. Xing Lü
6. Yuan Zhou
7. Zuo-nong Zhu
8. Zhenyun Qin

Citations in the corpus

• Riemann–Hilbert problems andN-soliton solutions for a coupled mKdV system (2018, background): “When the underlying matrix loop algebra in the zero curvature formulation is simple, the associated zero curvature equations yield classical soliton hierarchies [10]; when semisimple, the associated zero curvature equations yield a collection of different soliton hierarchies; and when non-semisimple”
• Application of the Riemann–Hilbert approach to the multicomponent AKNS integrable hierarchies (2019, background): “We point out that when the underlying matrix loop algebra in the zero curvature formulation is simple, the associated zero curvature equations engender typical integrable hierarchies [28,10]; when semisimple, the associated zero curvature equations generate a collection of different integrable hiera”
• Semidirect sums of Lie algebras and discrete integrable couplings (2006, background): “Very recently, we have proposed a relation between semi-direct sums of Lie algebras and integrable couplings of continuous soliton equations, which provides an interesting and systematic approach to integrable couplings of continuous soliton equations [15].”
• Long-Time Asymptotics of a Three-Component Coupled mKdV System (2019, background): “[40,41], a collection of different integrable hierarchies, and hierarchies of integrable couplings [42], 70”
• The inverse scattering transform and soliton solutions of a combined modified Korteweg–de Vries equation (2019, background): “When the underlying matrix loop algebra in the zero curvature formulation is simple, the associated zero curvature equations engender classical integrable hierarchies [7,13]; when semisimple, the associated zero curvature equations generate a collection of different integrable hierarchies; and when ”