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Number of results

Journal

2015 | 13 | 1 |

Article title

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

Content

Title variants

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.

Publisher

Journal

Year

Volume

13

Issue

1

Physical description

Dates

accepted
1 - 10 - 2015
online
23 - 11 - 2015
received
7 - 3 - 2015

Contributors

author
  • School of Mathematics
    and Physics, Bohai University, Jinzhou 121013, PR China
author
  • School of Mathematics and Statistics, Kashgar University,
    Kashgar 844066, Peoples’s Republic of China

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_phys-2015-0040
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