## 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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