Mixed spectral AKNS hierarchy from linear isospectral problem
and its exact solutions

• Authors: Sheng Zhang , Xu-Dong Gao
• Languages of publication: EN

Abstracts

EN

In this paper, the AKNS isospectral problem and
its corresponding time evolution are generalized by embedding
three coefficient functions. Starting from the generalizedAKNS
isospectral problem, a mixed spectralAKNS
hierarchy with variable coefficients is derived. Thanks to
the selectivity of these coefficient functions, the mixed
spectral AKNS hierarchy contains not only isospectral
equations but also nonisospectral equations. Based on a
systematic analysis of the related direct and inverse scattering
problems, exact solutions of the mixed spectral
AKNS hierarchy are obtained through the inverse scattering
transformation. In the case of reflectionless potentials,
the obtained exact solutions are reduced to n-soliton solutions.
This paper shows that the AKNS spectral problem
being nonisospectral is not a necessary condition to
construct a nonisospectral AKNS hierarchy and that the
inverse scattering transformation can be used for solving
some other variable-coefficient mixed hierarchies of
isospectral equations and nonisospectral equations.

Keywords

EN

mixed spectral AKNS hierarchy; spectral problem; exact solution; soliton solution; inverse scatteringtransformation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

accepted

1 - 10 - 2015

online

23 - 11 - 2015

received

7 - 3 - 2015

Contributors

author

Sheng Zhang

• School of Mathematics
  and Physics, Bohai University, Jinzhou 121013, PR China

author

Xu-Dong Gao

• School of Mathematics and Statistics, Kashgar University,
  Kashgar 844066, Peoples’s Republic of China

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Identifiers

DOI

10.1515/phys-2015-0040