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Generalized Matrix Exponential Solutions to the AKNS Hierarchy

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  • Jian-bing Zhang
  • Canyuan Gu
  • Wen-Xiu Ma

Abstract

Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different kinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy are also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure.

Suggested Citation

  • Jian-bing Zhang & Canyuan Gu & Wen-Xiu Ma, 2018. "Generalized Matrix Exponential Solutions to the AKNS Hierarchy," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-9, February.
    • Handle: RePEc:hin:jnlamp:1375653
    DOI: 10.1155/2018/1375653
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