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Journal
2015 | 13 | 1 |
Article title

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

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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
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Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0040
Identifiers
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