THERMAL SCIENCE
International Scientific Journal
INVERSE SCATTERING TRANSFORM FOR A NEW NON-ISOSPECTRAL INTEGRABLE NON-LINEAR AKNS MODEL
ABSTRACT
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.
KEYWORDS
PAPER SUBMITTED: 2017-04-12
PAPER REVISED: 2017-05-16
PAPER ACCEPTED: 2017-05-26
PUBLISHED ONLINE: 2017-12-02
THERMAL SCIENCE YEAR
2017, VOLUME
21, ISSUE
Supplement 1, PAGES [S153 - S160]
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