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A New Approach for Generating the TX Hierarchy as well as Its Integrable Couplings

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  • Guangming Wang

Abstract

Tu Guizhang and Xu Baozhi once introduced an isospectral problem by a loop algebra with degree being λ, for which an integrable hierarchy of evolution equations (called the TX hierarchy) was derived under the frame of zero curvature equations. In the paper, we present a loop algebra whose degrees are 2λ and 2λ + 1 to simply represent the above isospectral matrix and easily derive the TX hierarchy. Specially, through enlarging the loop algebra with 3 dimensions to 6 dimensions, we generate a new integrable coupling of the TX hierarchy and its corresponding Hamiltonian structure.

Suggested Citation

  • Guangming Wang, 2014. "A New Approach for Generating the TX Hierarchy as well as Its Integrable Couplings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:357621
    DOI: 10.1155/2014/357621
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    References listed on IDEAS

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    1. Xia, Tiecheng & You, Fucai & Chen, Dengyuan, 2006. "A generalized cubic Volterra lattice hierarchy and its integrable couplings system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 153-158.
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