Inverse scattering transform for a new non-isospectral integrable non-linear AKNS model
Constructing integrable systems and solving non-linear partial differential equations are important and interesting in non-linear science. In this paper, Ablowitz-Kaup-Newell-Segur (AKNS)’s linear isospectral problem and its accompanied time evolution equation are first generalized by embed...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
VINCA Institute of Nuclear Sciences
2017-01-01
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Series: | Thermal Science |
Subjects: | |
Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-9836/2017/0354-983617153G .pdf |
Summary: | Constructing integrable systems and solving non-linear partial differential
equations are important and interesting in non-linear science. In this
paper, Ablowitz-Kaup-Newell-Segur (AKNS)’s linear isospectral problem and
its accompanied time evolution equation are first generalized by embedding a
new non-isospectral parameter whose varying with time obeys an arbitrary
smooth enough function of the spectral parameter. Based on the generalized
AKNS linear problem and its evolution equation, a new non-isospectral Lax
integrable non-linear AKNS model is then derived. Furthermore, exact
solutions of the derived AKNS model is obtained by extending the inverse
scattering transformation method with new time-varying spectral parameter.
In the case of reflectinless potentials, explicit n-soliton solutions are
finally formulated through the obtained exact solutions. |
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ISSN: | 0354-9836 2334-7163 |